3.1 Graphing Quadratic Functions Practice
Vertex Form y = a(x - h)2 + k
1. y = (x + 4)2 - 9
2. y = -(x - 3)2 +1
y
(3,1)
1
y
9
-1
1
2
8
7
(0,7)
(2,0)
3
4
x
(4,0)
5
6
7
8
9
-1
6
5
-2
4
-3
3
2
-4
1
-9
-8
-7
(-7,0)
-6
-5
-4
-3
-2
-1
(-1,0)
x
1
-5
-1
-2
-6
-3
-4
-7
-5
-6
-8
(0,-8)
-7
-9
-8
(-4,-9)
-9
a = _____ h = _____ k = _____
a = _____ h = _____ k = _____
a. vertex
(
,
b. x-intercept(s)
c. y-intercept
)
(
(
d. root(s) or zero(es)
a. vertex
,
,
) (
,
)
,
b. x-intercept(s)
)
x=
(
c. y-intercept
(
(
d. root(s) or zero(es)
,x=
)
,
,
) (
,
)
)
x=
,x=
e. Since the a term is (positive, negative), the graph
opens (up, down), and the vertex is the (maximum,
minimum) value of the function.
e. Since the a term is (positive, negative), the graph
opens (up, down), and the vertex is the (maximum,
minimum) value of the function.
f. Sketch the Line of Symmetry.
f. Sketch the Line of Symmetry.
g. Its equation is x = _________
g. Its equation is x = _________
h. What is the name of the point where the
y-value or the function changes direction?
h. What is the name of the point where the
y-value or the function changes direction?
______________________________
______________________________
i. What are the other 3 names for x-intercepts?
i. What are the other 3 names for roots?
__________ , __________, ____________
__________ , ____________, ____________
j. State the domain in inequality and interval notation:
j. State the domain in inequality and interval notation:
k. State the range in inequality and interval notation:
k. State the range in inequality and interval notation:
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Standard Form f ( x)  ax2  bx  c
4. y   x 2  8 x  12
3. y  x 2  4 x
y
(-4,4)
y
4
3
5
2
4
1
-9
-8
-7
3
-6
(-6,0)
-5
-4
-3
-2
x
(-2,0)
-1
1
-1
-2
2
-3
1
-4
-5
-4
-3
-2
(0,0)
-1
1
2
3
4
(4,0)
x
-5
5
-6
-7
-1
-8
-2
-9
-1 0
-3
-1 1
(2,-4)
-4
-1 2
(0,-12)
-1 3
-5
-1 4
The quadratic term
The linear term
The constant
a. y-intercept
(
b. x-intercept(s)
,
(
c. root(s) or zero(es)
d. vertex
(
,
The quadratic term
The linear term
The constant
a = ____
b = ____
c = ____
a. y-intercept
)
,
) (
x=
,
(
b. x-intercept(s)
)
,
(
c. root(s) or zero(es)
,x=
d. vertex
)
(
a = ____
b = ____
c = ____
,
)
,
) (
x=
,
)
,x=
)
e. Since the a term is (positive, negative), the graph
opens (up, down), and the vertex is the (maximum,
minimum) value of the function.
e. Since the a term is (positive, negative), the graph
opens (up, down), and the vertex is the (maximum,
minimum) value of the function.
f. State the domain in inequality and interval notation:
f. State the domain in inequality and interval notation:
g. State the range in inequality and interval notation
g. State the range in inequality and interval notation
** When the range is (, #] does the quadratic function have a minimum, maximum or neither?
** When the range is [#, ) does the quadratic function have a minimum, maximum or neither?
You can use the MINUMUM or MAXIMUM feature on a graphing calculator to find the minimum or maximum of a
quadratic function. This involves defining an interval that includes the vertex of the parabola. A lower bound is an x-value
left of the vertex, and an upper bound is an x-value right of the vertex.
Step 1. Graph the function so that the vertex of the parabola is visible.
Step 2. Select 3:minimum or 4 maximum from the CALC menu.
Step 3 Using the arrow keys, locate a left bound and press ENTER
Step 4.Using the arrow keys, locate a right bound and press ENTER twice. The cursor appears on the maximum or
minimum of the function. The maximum or minimum value of the function is the
y-coordinate of the vertex point.
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