Quadratic Functions Worksheets With Answer Key - Pre-Calculus, Michigan State University Page 2
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2
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62
The General Form of a Quadratic Function is
y
=
f
(
x
)
=
ax
+
bx
+
c
, where a ≠ 0
Graph is a parabola with vertex at
If a > 0, then the parabola opens up.
2
b
b
b
b
−
−
−
−
,
f
or
,
c
.
If a < 0, then the parabola opens down.
2
a
2
a
2
a
4
a
b
=
−
Graph is symmetric to the line
x
.
y-intercept is (0, c).
2
a
2
Example 2: Graph the quadratic function
(
)
=
−
2
−
8
.
f
x
x
x
y
Steps:
9
1. Opens up or down?
8
7
(a > 0 or a < 0)
6
5
2. Find vertex (h, k).
4
3
2
Domain:
1
x
Range:
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
−1
Eq. of line of symmetry:
−2
−3
−4
3. Find x-intercepts.
−5
−6
(Let y = 0.)
−7
−8
−9
4. Find y-intercept.
−10
(Let x = 0.)
5. Graph the parabola.
Plot intercepts, vertex and
additional point(s).
(Use line/axis of symmetry.)
y
2
Example 3: For the parabola defined by
f
(
x
)
=
x
−
6
x
+
11
, find
6
(a) the coordinates of the vertex.
4
(b) the x- and y-intercepts.
2
(c) the domain and range.
x
−1
1
2
3
4
5
6
7
8
(d) Sketch the graph of f.
−2
Page 2 (Section 3.2)
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