Name
LESSON
5-2
Date
Class
Reteach
Properties of Quadratic Functions in Standard Form
You can use the properties of a parabola to graph a quadratic function in standard form:
f x ax 2 bx c, a 0.
Property
Example: f x x 2 2x 2
a 0: opens upward
a 1, b 2, c 2
a 0: opens downward
a 0, so parabola opens downward.
b
Axis of symmetry: x ___
2a
b , f ___
b
Vertex: ___
2a
2a
2 b ______
Axis of symmetry: x ___
1
2a
2 1 b f 1 1 1 2 2 1 2 3
f ___
2a
Vertex: 1, 3 y-intercept is 2, so 0, 2 is a point on the graph.
y-intercept: c
2
To graph f x x 2x 2:
Y
1.
Plot vertex.
2.
Sketch axis of symmetry through vertex.
3.
Plot y-intercept.
4.
Use symmetry to plot 2, 2 .
5.
Sketch graph.
X
2
Use the properties of a parabola to graph f x x 4x 3.
1. a 1
,b
4 , c 3
Upward
2. The graph opens
b 3. Axis of symmetry: x ___
2a
b f 2 1
4. f ___
2a
5. Vertex:
Y
.
x2
2, 1 X
6. y-intercept:
3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-2_rt.indd 14
14
Holt Algebra 2
12/15/05 4:36:22 PM
Process Black
Name
LESSON
5-2
Date
Class
Reteach
Properties of Quadratic Functions in Standard Form
(continued)
The maximum or the minimum value of a parabola is the y-value of the vertex,
b . If the parabola opens upward, a 0, then it is a minimum value. If the
or f ___
2a
parabola opens downward, a 0, then it is a maximum value.
f x 2x 2 4x 3
2
f x 3x 12x 1
a 2: Find maximum.
a 3: Find minimum.
b for a 2 and b 4.
Evaluate ___
2a
b ______
4
___
1
2a
2 2 b f 1 f ___
2a
b for a 3 and b 12.
Evaluate ___
2a
b ____
12 2
___
2a
2 3 b f 2 f ___
2a
2 1 2 4 1 3 1
3 2 2 12 2 1 11
Maximum value is 1.
Minimum value is 11.
Range: { y y 1 }
Range: { y y 11 }
All other y-values must be less
than or equal to the maximum.
All other y-values must be greater
than or equal to the minimum.
Find the minimum or maximum value of each function.
Then state the range of each function.
7. f x 2x 2 8x 9
Minimum or maximum?
8 b _____
___
2a
2 2 b f ___
2a
Range:
8. f x 3x 2 6x 4
Minimum
Minimum or maximum?
2
b ___
2a
1
a207c05-2_rt.indd 15
1
b f ___
2a
{ y y 1 }
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Range:
15
Maximum
1
{ y y 1 }
Holt Algebra 2
12/15/05 4:36:25 PM
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