Quadratic functions
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Transcript of Quadratic functions
![Page 1: Quadratic functions](https://reader034.fdocuments.us/reader034/viewer/2022052623/559c93ca1a28ab50098b469d/html5/thumbnails/1.jpg)
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General Formf(x) = ax2c
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Standard Formf(x) = a (x k
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Transforming Quadratic Functions
from General Form
to Standard Form
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STEPS:
1. Factor out a from the first
two terms.
2. Complete the square.
3. Factor and combine.
![Page 6: Quadratic functions](https://reader034.fdocuments.us/reader034/viewer/2022052623/559c93ca1a28ab50098b469d/html5/thumbnails/6.jpg)
f(x) = ax2 + bx + c
Step 1: Factor out a from the first
two terms.
f(x) = a (x2 +𝑏𝑥
𝑎) + c
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Step 2: Complete the square.
f(x) = a [x2 +bx + ( 𝑏
𝑎𝑥)2] + c - a(
𝑏
2𝑎)2
f(x) = a [x2 + bx +( 𝑏
𝑎𝑥)2] + c -
𝑎𝑏2
4𝑎2
f(x) = a [x2 + bx +( 𝑏𝑥)2] + c -
𝑏2
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Step 3: Factor and combine.
f(x) = a (x + 𝑏
2𝑎)2 +
4𝑎𝑐−𝑏2
4𝑎
h= -𝑏
2𝑎and k =
4𝑎𝑐−𝑏2
4𝑎
f(x) = a (x - h)2 + k
![Page 9: Quadratic functions](https://reader034.fdocuments.us/reader034/viewer/2022052623/559c93ca1a28ab50098b469d/html5/thumbnails/9.jpg)
Examples
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f(x) = x2 – 8x + 3 a = 1
f(x) = (x2 – 8x) + 3
f(x) = (x2 –8x + ( 8
2)2) + 3 - (
8
2)2
f(x) = (x2 – 8x + (4)2) + 3 – (4)2
f(x) = (x2 – 8x + 16) + 3 – 16
f(x) = (x – 4) 2 – 13
![Page 11: Quadratic functions](https://reader034.fdocuments.us/reader034/viewer/2022052623/559c93ca1a28ab50098b469d/html5/thumbnails/11.jpg)
f(x) = 2 x2 + 5𝑥 – 1 a = 2
f(x) = 2 (x2 + 5
2𝑥 ) – 1
f(x) = 2 [x2 + 5
2𝑥 + (
25
16)] – 1 -
25
8
f(x) = 2 (x + 5
4)2 + (
−8−25
8)
f(x) = 2 (x + 5
4)2 + (
−33
8)
![Page 12: Quadratic functions](https://reader034.fdocuments.us/reader034/viewer/2022052623/559c93ca1a28ab50098b469d/html5/thumbnails/12.jpg)
1. f(x) = x2 - 12x + 4
2. f(x) = 5x2 + 20x -12
3. f(x) = x2 + 3x + 36
4. f(x) = 4x2 + 2x + 9
5. f(x) = 3x2 + 6x + 2
ActivityTransform the following quadratic functions
into standard form.