Use the information on page 306 to explain how the graph of y = x can be used to graph any quadratic function.

Writing in MathUse the information on page 306 to explain how the graph of y = xcan be  used to graph any quadratic function. Include a description of the effects produced by changing a, h, and k in the equation y = a(x ­ h)^2 + k, and a comparison of the graph of y = x and the graph of y = a(x ­ h)^2+ k using values of your own choosing for a, h, and k.

5-7
Analyzing Graphs of
Quadratic Functions
Concepts in Motion
Interactive Lab algebra.com
Main Ideas
• Analyze quadratic
functions of the form
y = a(v – Mak
Write a quadratic
function in the form
y = (x – 1)”+k
New Vocabulary
vertex form
GET READY for the Lesson
A family of graphs is a group of graphs
that displays one or more similar
characteristics. The graph of y = ris
called the parent graph of the family of
quadratic functions.
The graphs of other quadratic
functions such as y = x2 + 2 and
y = (x – 3)2 can be found by
transforming the graph of y = x?
o
X=0
(0,2)
X=0
X=3
Analyze Quadratic Functions Each
Equation
Aads of
function above can be written in the
form y = (x – h)2 + k, where (h, k) is
y=r’ or
y = (x – 02+0
(0,0)
the vertex of the parabola and x =lis
y=x+2 or
its axis of symmetry. This is often
y = -02+2
referred to as the vertex form of a
y=(x-3) or
quadratic function.
(3.0)
y=(x-3) + 0
Recall that a translation slides a figure
without changing its shape or size. As the values of h and k change, the
graph of y = 2(x – h)2 + k is the graph of y = x- translated:
. || units left if k is negative or | h| units right if k is positive, and
• \k/ units up if k is positive or | k/ units down if k is negative.
EXAMPLE Graph a Quadratic Equation in Vertex Form
Analyze y = (x + 2)2 + 1. Then draw its graph.
This function can be rewritten as y = [1 – (-2)2 + 1. Then h = -2
and k = 1. The vertex is at (h, k) or (-2, 1), and the axis of symmetry
is x = -2. The graph is the graph of y = x- translated 2 units left and
1 unit up.
Now use this information to draw the graph.
Step 1 Plot the vertex, (-2,1).
Step 2 Draw the axis of symmetry, * = -2. y= x + 2)* +1N
1422
Step 3 Use symmetry to complete the graph. (-2.12
JTOHECK Your Progress
1. Analyze y = (x – 3)2 – 2. Then draw its graph.
10, 5)
286 Chapter 5 Quadratic Functions and Inequalities