2.2 - Quadratic Functions in Intercept & Standard Forms...Obj: Idenify properties of quads in...
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2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018 Ex 2: Graph the function. Label the roots(xint), vertex, and axis of symmetry. f(x) = 1/4(x 6)(x 2) Roots: Axis of Symmetry: Vertex: Domain: ____________ Range: _____________
Transcript of 2.2 - Quadratic Functions in Intercept & Standard Forms...Obj: Idenify properties of quads in...
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Ex 2: Graph the function. Label the roots(xint), vertex, and axis of symmetry.
f(x) = 1/4(x 6)(x 2)Roots:
Axis of Symmetry:
Vertex:
Domain: ____________
Range: _____________
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Ex 3: Tell whether the graph opens up or down, the identify the roots(xint) for each functions.
a) f(x) = (x + 8)(x 4)
b) y = 2x(x + 7)
c) g(x) = 2/3(x + 3)2
HINT: For roots, just set each expression containing x equal to zero and solve.
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Minimum or Maximum value: the yvalue of the vertex.
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Ex 4: Find the min/max value for each function.
a) f(x) = (x + 8)(x 4)
b) y = 0.4(x + 3)2
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
2.2 - Quadratic Functions in Standard Form• Standard Form and Properties:• f(x) = ax2 + bx + c where a 0• Gives us the yintercept @ (0, c)• Can find an axis of symmetry by calculating:
• The graph is:• narrower when |a| > 1• wider when |a| < 1
Obj: Idenify properties of quads in standard form and graph.
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Characteristics of :If a>0: graph opens ____.
If a<0: graph opens ____.
Axis of symmetry:
Vertex:
yintercept is c.
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Ex 1: Graph y = 3x2 12x + 1
x
y
5) Domain:
6) Range:
Does this graph open up or down?
1) Axis of symmetry:
2) Find the vertex:
3) Find the yintercept:
4) Reflect the yintercept.
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Ex 2: Graph h(x) = 1/3x2 + 2x 1
x
y
5) Domain:
6) Range:
Does this graph open up or down?
1) Axis of symmetry:
2) Find the vertex:
3) Find the yintercept:
4) Reflect the yintercept.
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
Ex 3: Tell whether the function has a minimum or maximum value. Then find that value.
y = 3x2 + x 2
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
You Try! ANSWERS1. 2.
(a) Opens up or down?
(b) Axis of symmetry:
(c) Vertex:
(d) Minimum or Maximum?
(e) Min/Max value:
(a) Opens up or down?
(b) Axis of symmetry:
(c) Vertex:
(d) Minimum or Maximum?
(e) Min/Max value:
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
What does each form give us?
1. Vertex form: y = a(x h)2 + kGives us the:
2. Intercept form: y = a(x p)(x q)Gives us the:
3. Standard form: y = ax2 + bx + cGives us the:
2.2 Quadratic Functions in Intercept & Standard Forms September 21, 2018
2.2 Homework MUST BE DONE ON A SEPARATE SHEET OF PAPER NO EXCEPTIONS!
DUE MONDAY 9/24
Graph the function. Label the vertex and axis of symmetry.
1. f(x) = 4(x 2)2 + 4 2. y = 1/2(x 3)2
Graph the function. Label the roots, vertex, and axis of symmetry.
3. h(x) = (x + 2)(x 6) 4. f(x) = 2(x 5)(x 1)
Graph the function. Label the yintercept and write the domain and range.
5. f(x) = x2 6x + 3 6. y = 6x2 5
Calculate the axis of symmetry for each function, and give the min/max value (example: max @ y = 18).
7. g(x) = (x + 5)(x 3) 8. y = 2x2 x + 7 9. c(x) = 0.75(x 8)2
Identify the roots for each function.
10. y = 1/4(x + 2)(x 2) 11. h(x) = 4(x 9)2 12. f(x) = 4x(x + 7)
