Download Standard Form of a Quadratic Function

4-2
Standard Form of a
Quadratic Function
PART 1
Vocabulary
Review
1. Circle the functions in standard form.
y 5 2x2 2 4x 1 2
y 5 13 (x 2 4)
y 5 24x 1 1
5
y 5 223 x 2 3 x 1 4
Write each equation in standard form.
2. x 1 2y 5 17
3. 2x 5 5
4. 5 2 x 5 y 1 2
Vocabulary Builder
Standard Form of a
Quadratic Function
quadratic (adjective) kwah DRAT ik
y ax2 bx c,
Related Words: parabola, vertex, axis of symmetry
Examples: quadratic functions, y 5 x2 , y 5 23x2 1 7, f (x) 5 2x2 1 5x 2 4,
g(x) 5 12 (x 2 4)2 1 5
Nonexamples: not quadratic functions, y 5
2x2
x2 1 5x 1 10
1
,
3x
1 4x 1 5
Use Your Vocabulary
5. Circle the graphs of quadratic functions.
y
y
y
x
x
x
Chapter 4
HSM11A2LC_C04_182-183.indd 182
y
x
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
a0
Definition: A quadratic function is a function that can be
written in the form y 5 ax2 1 bx 1 c where a 2 0. The
graph of a quadratic function is a parabola.
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Problem 1 Finding the Features of a Quadratic Function
Got It? What are the vertex, axis of symmetry, maximum and minimum values,
and range of y 5 23x2 2 4x 1 6?
6. Circle the graph of y 5 23x2 2 4x 1 6.
7. Draw and label the axis of symmetry on the graph you circled in Exercise 6.
8. Circle and label the maximum or minimum value on the graph.
9. Circle the range of the function.
y $ 5.0
y # 6.0
all real numbers # 7.3
all real numbers # 9.2
Properties Quadratic Function in Standard Form
• The graph of f (x) 5 ax2 1 bx 1 c, a 2 0, is a parabola.
• If a . 0, then the parabola opens upward. If a , 0, then the parabola opens downward.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
b
• The axis of symmetry is the line x 5 22a
.
b
• The x-coordinate of the vertex is 2a
. The y-coordinate of the vertex is the y-value of the function for
b
b
x 5 22a
, or y 5 f Q22a
R.
• The y-intercept is (0, c).
y ax 2 bx c, a0
y
x b
2a
y ax 2 bx c,, a0
y
b , f b
2a
2a (0, c)
(0, c)
O
x
x
O
x b
2ab , f 2ab 2a
10. The axis of symmetry of y 5 x2 1 6x 1 5 is the line x 5 23 / 3 / 5 .
11. The y-intercept of the graph of f (x) 5 5x2 2 3x 2 4 is Q
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HSM11A2LC_C04_182-183.indd 183
,
R.
Lesson 4-2, Part 1
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Problem 2
Graphing a Function of the Form y 5 ax2 1 bx 1 c
Got It? What is the graph of y 5 22x 2 1 2x 2 5?
8
12. Identify a, b, and c.
a5
b5
4
c5
b
13. The axis of symmetry is x 5 22a 5 2
5
2?
.
4
2
R 5 22 Q
5
R 1 2Q
1
2
4
4
R25
8
255
15. The vertex is Q
R.
,
16. The y-intercept is Q 0,
of symmetry is Q
x
O
2
14. Subtitute to find the y-coordinate of the vertex.
fQ
y
,
R . The reflection of the y-intercept across the axis
R.
17. Since a , / . 0, the graph opens downward / upward .
18. Use your answers to Exercises 13–17 to graph the function.
Error Analysis A student graphed the function
y 5 2x2 2 4x 2 3. Find and correct the error.
b
x = -4 = -1
b
19. The vertex of y 5 ax2 1 bx 1 c is Q22a , f Q22a RR .
Find the x- and y-coordinates of the vertex of
y5
2x2
6
2(2)
2 4x 2 3.
y = 2(-1)2 - 4(-1) - 3
=2+4-3
=3
vertex (-1, 3)
(1, 3) 2
4 2
0
2
y
4
20. Find the y-intercept of y 5
2x2
2 4x 2 3.
2
2
21. Describe the student’s error and graph the function correctly.
________________________________________________________
O
2
4
x
2
4
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Lesson Check • Do you UNDERSTAND?
________________________________________________________
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