11 x1 t10 01 graphing quadratics (2013)
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Transcript of 11 x1 t10 01 graphing quadratics (2013)
![Page 1: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/1.jpg)
The Quadratic Polynomial and the Parabola
![Page 2: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/2.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial –
![Page 3: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/3.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
![Page 4: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/4.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function –
![Page 5: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/5.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
![Page 6: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/6.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation –
![Page 7: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/7.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c
![Page 8: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/8.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c Coefficients –
![Page 9: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/9.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –
![Page 10: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/10.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –
Indeterminate –
![Page 11: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/11.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
![Page 12: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/12.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots –
![Page 13: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/13.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equation
![Page 14: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/14.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equationZeroes –
![Page 15: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/15.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function
![Page 16: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/16.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function
2e.g. Find the roots of 1 0x
![Page 17: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/17.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function
2e.g. Find the roots of 1 0x 2
2
1 01
xx
![Page 18: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/18.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function
2e.g. Find the roots of 1 0x 2
2
1 01
xx
1x
![Page 19: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/19.jpg)
The Quadratic Polynomial and the Parabola
Quadratic polynomial – 2ax bx c
Quadratic function – 2y ax bx c
Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –
Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function
2e.g. Find the roots of 1 0x 2
2
1 01
xx
1x the roots are 1 and 1x x
![Page 20: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/20.jpg)
Graphing Quadratics
![Page 21: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/21.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola.
![Page 22: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/22.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
![Page 23: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/23.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
a
![Page 24: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/24.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x
![Page 25: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/25.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
![Page 26: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/26.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up
![Page 27: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/27.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up
y
x
![Page 28: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/28.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
![Page 29: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/29.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave down
![Page 30: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/30.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc
![Page 31: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/31.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y intercept
![Page 32: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/32.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots)
![Page 33: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/33.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
![Page 34: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/34.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
![Page 35: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/35.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
= axis of symmetry
![Page 36: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/36.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
= axis of symmetry Note: AOS is the average of the zeroes
![Page 37: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/37.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
= axis of symmetry Note: AOS is the average of the zeroes
vertex
![Page 38: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/38.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
= axis of symmetry Note: AOS is the average of the zeroes
vertex x value is the AOS
![Page 39: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/39.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
= axis of symmetry Note: AOS is the average of the zeroes
vertex x value is the AOSy value is found by substituting AOS into the function.
![Page 40: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/40.jpg)
Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c
ay
x0a
concave up0a
y
x
concave downc = y interceptzeroes (roots) = x intercepts
2bxa
= axis of symmetry Note: AOS is the average of the zeroes
vertex x value is the AOSy value is found by substituting AOS into the function.
(It is the maximum/minimum value of the function)
![Page 41: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/41.jpg)
e.g. 2Graph 8 12y x x
![Page 42: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/42.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0
y
x
![Page 43: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/43.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up
y
x
![Page 44: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/44.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12
y
x
2 8 12y x x
![Page 45: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/45.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
y
x
![Page 46: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/46.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
y
x
12
![Page 47: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/47.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes y
x
12
![Page 48: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/48.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x y
x
12
2 8 12y x x
![Page 49: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/49.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
y
x
12
2 8 12y x x
![Page 50: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/50.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
y
x
12
2 8 12y x x
![Page 51: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/51.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
y
x
12
2 8 12y x x
![Page 52: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/52.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
y
x
12
–2 –6
2 8 12y x x
![Page 53: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/53.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS
y
x
12
–2 –6
2 8 12y x x
![Page 54: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/54.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
y
x
12
–2 –6
2 8 12y x x
![Page 55: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/55.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
y
x
12
–2 –6
2 8 12y x x
![Page 56: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/56.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
y
x
12
–2 –6
2 8 12y x x
![Page 57: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/57.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
y
x
12
–2 –6
2 8 12y x x
![Page 58: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/58.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
y
x
12
–2 –6
2 8 12y x x
![Page 59: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/59.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
vertex
y
x
12
–2 –6
2 8 12y x x
![Page 60: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/60.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
vertex 24 8 4 12y
y
x
12
–2 –6
2 8 12y x x
![Page 61: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/61.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
vertex 24 8 4 12y
4
y
x
12
–2 –6
2 8 12y x x
![Page 62: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/62.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
vertex 24 8 4 12y
4 vertex is 4, 4
y
x
12
–2 –6
2 8 12y x x
![Page 63: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/63.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
vertex 24 8 4 12y
4 vertex is 4, 4
y
x
12
–2 –6
(–4, –4)
2 8 12y x x
![Page 64: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/64.jpg)
e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y
zeroes 2 8 12 0x x 6 2 0x x
6 or 2x x
intercepts are
6,0 and 2,0x
AOS2
bxa
824
OR6 22
x
4
vertex 24 8 4 12y
4 vertex is 4, 4
y
x
12
–2 –6
(–4, –4)
2 8 12y x x
![Page 65: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/65.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
![Page 66: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/66.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
![Page 67: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/67.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
![Page 68: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/68.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2
![Page 69: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/69.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
c) roots 2 and 8 and vertex (5,3)
2 10 16y a x x
25,3 : 3 5 10 5 16a
3 913
a
a
21 10 163
y x x
![Page 70: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/70.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
3 2 3 2 3 2 3 2
![Page 71: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/71.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)
![Page 72: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/72.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)
2 10 16y a x x
![Page 73: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/73.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)
2 10 16y a x x
25,3 : 3 5 10 5 16a
![Page 74: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/74.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)
2 10 16y a x x
25,3 : 3 5 10 5 16a
3 913
a
a
![Page 75: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/75.jpg)
(ii) Find the quadratic with;a) roots 3 and 6
2 9 18y a x x
6 3 6 3
b) monic roots 3 2 and 3 2 2 6 7y x x
3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)
2 10 16y a x x
25,3 : 3 5 10 5 16a
3 913
a
a
21 10 163
y x x
![Page 76: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/76.jpg)
(iii) Solve;2) 5 6 0a x x
![Page 77: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/77.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
![Page 78: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/78.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2
![Page 79: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/79.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2
![Page 80: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/80.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
![Page 81: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/81.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
![Page 82: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/82.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
![Page 83: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/83.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
![Page 84: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/84.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x 2 3 4 0x x
![Page 85: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/85.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
4 1 0x x
2 3 4 0x x
![Page 86: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/86.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
4 1 0x x
y
x1–4
2 3 4 0x x
![Page 87: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/87.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
4 1 0x x
y
x1–4
2 3 4 0x x
![Page 88: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/88.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
4 1 0x x
y
x1–4
Q: for what values of x is theparabola below the x axis?
2 3 4 0x x
![Page 89: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/89.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
4 1 0x x
y
x1–4
Q: for what values of x is theparabola below the x axis?
2 3 4 0x x
![Page 90: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/90.jpg)
(iii) Solve;2) 5 6 0a x x
2 3 0x x
y
x–3 –2 Q: for what values of x is the
parabola above the x axis?
3 or 2x x
2) 3 4b x x
4 1 0x x
y
x1–4
Q: for what values of x is theparabola below the x axis?
4 1x
2 3 4 0x x
![Page 91: 11 x1 t10 01 graphing quadratics (2013)](https://reader034.fdocuments.us/reader034/viewer/2022051817/547c9b475906b54d378b4576/html5/thumbnails/91.jpg)
Exercise 8A; 1adf, 2adf, 3bd, 4bd, 5c, 6ade, 7d, 9ace, 12c,13b, 14a