Quadratic Functions Worksheets With Answer Key - Pre-Calculus, Michigan State University
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63.2 Quadratic Functions
In this section you will learn to:
• recognize the characteristics of quadratics functions
• find the vertex of a parabola
• graph quadratic functions
• apply quadratic functions to real world problems
• solve maximum and minimum problems
Graphs of Quadratic Functions:
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
x
−1
1
2
3
4
5
6
7
8
−1
1
2
3
4
5
6
7
8
−1
−1
−2
−2
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The Standard Form of a Quadratic Function is
y
=
f
(
x
)
=
a
(
x
−
h
)
+
k
, where a ≠ 0
Its graph is a parabola with vertex at (h, k).
If a > 0, then the parabola opens up.
Its graph is symmetric to line x = h
If a < 0, then the parabola opens down.
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Example 1: Graph the quadratic function
f
(
x
)
=
−
(
x
+
) 2
+
. 3
y
Steps:
7
1. Opens up or down?
6
5
(a > 0 or a < 0)
4
3
2. Find vertex (h, k).
2
Find the domain.
1
Find the range.
x
−7
−6
−5
−4 −3 −2 −1
1
2
3
4
5
6
7
8
−1
3. Find x-intercepts.
−2
(Let y = 0.)
−3
−4
4. Find y-intercept.
−5
(Let x = 0.)
−6
−7
5. Graph the parabola.
−8
Plot intercepts, vertex and
additional point(s). (Use line/axis of symmetry.)
Page 1 (Section 3.2)
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