1. Graphing f(x) = (x - h) + k 3.3A 2 Chapter 3 Quadratic Functions
MATHPOWERTM 11, WESTERN EDITION
3.3A.1

2. Graphing f(x) = (x - h)2 Comparing f(x) = (x - h)2 with f(x) = x 2:
(-2, 0)
(2, 0)
x y
f(x) = (x - 2)2
f(x) = (x + 2)2
f(x) = x2
Vertex is (-2, 0)
Axis of symmetry is x + 2 = 0
Minimum value of
y = 0, when x = -2
Vertex is (2, 0)
Axis of symmetry is x - 2 = 0
Minimum value of
y = 0, when x = 2
3.3A.2

3. Graphing f(x) = (x - h)2 [cont’d]
Graph f(x) = (x - 4)2.
The vertex is (4, 0).
The axis of symmetry
is x - 4 = 0.
The graph opens upwards.
It has a minimum value
of y = 0, when x = 4. 1 2 3 4
f(x) = x2
f(x) = (x - 4)2
The domain is
all real numbers.
The y-intercept is 16.
The range is y > 0.
The x-intercept is (4, 0).
3.3A.3

4. f(x) = a(x - h)2 + k The Standard Form of the Quadratic Function
Horizontal
shift
Stretch
factor
Vertical
shift
f(x) = a(x - h)2 + k
Indicates direction
of opening
Coordinates of
the vertex are (h, k)
If a > 0, the graph opens
up and there is a
minimum value of y.
If a < 0, the graph opens
down and there is a
maximum value of y.
Axis of symmetry
is x - h = 0
3.3A.4

5. Graphing f(x) = a(x - h)2 + k
When a > 0:
Move over 1 and
up 2, to account
for the stretch
factor of 2.
Graph f(x) = 2(x - 3)2 + 4.
The vertex will
be the point
(3, 4).
1. Think of the critical
point for the parabola
f(x) = x2. 4 3
Move
4 units
up.
f(x) = 2(x - 3)2 + 4 2
2. Move that point to the
new vertex (h, k). 1
(0, 0) 1 2 3
3. Consider the “a” value
and plot your next
reference points.
Move 3 units
to the right.
3.3A.5

6. Graphing f(x) = a(x - h)2 + k [cont’d]
When a < 0:
The new vertex
is (3, 4).
Graph f(x) = -2(x - 3)2 + 4.
f(x) = -2(x - 3)2 + 4
Move over 1 and
down 2, to account
for the stretch
factor and the fact
that a < 0.
Move
4 units
up.
(0, 0)
Move 3 units
to the right.
3.3A.6

7. Finding the Intercepts
Given the function y = 2(x - 4)2 - 12:
y = 2(0 - 4)2 - 12
y = 2(16) - 12
y = 20
Find the y-intercept.
The y -intercept
is 20.
Let x = 0.
2(x - 4) = 0
2(x - 4)2 = 12
(x - 4)2 = 6
x - 4 = + √ 6
Find the x-intercepts.
The x-intercepts are
4 + √ 6 and 4 - √ 6 .
Let y = 0.
x = 4 + √ 6
3.3A.7