Algebra 1 Common Core Student Edition, Grade 8-9

Key Concept Graph of a Quadratic Function

The graph of y = a x 2 + bx + c, where a ¥= 0, has the line x = as its axis of

symmetry. The x-coordinate of the vertex is ^r.

ThinK
How are the vertex
and the axis of
symmetry related?
The ve rte x is on th e axis
o f sym metry. You can
use th e e q u a tio n fo r th e
axis o f s ym m etry to fin d
th e x -c o o rd in a te o f th e
vertex.

When you substitute x = 0 into the equation y = ax2 + bx + c, you get y = c. So the

y-intercept of a quadratic function is c. You can use the axis of symmetry and the

y-intercept to help you graph a quadratic function.

Gr ap h i n g y = a x 2 + bx + c

What is the graph of the function y = x2 - 6x + 4?

St e p 1 Find the axis of symmetry and the coordinates of the vertex.

x = ^ = 3 Find the equation o f the axis o f symmetry.

The axis of symmetry is x = 3. So the x-coordinate of the vertex is 3.

y = x2 - 6x + 4

= 32 - 6(3) + 4 Substitute 3 fo r x to find the y-coordinate o f the vertex.

= - 5 Simplify.

The vertex is (3, —5).

St e p 2 Find two other points on the graph.

Find the y-intercept. When x = 0, y = 4, so one point is (0, 4).

Find another point by choosing a value for x on the same side of the vertex as

the y-intercept. Let x = 1.

y = x2 - 6x + 4

= l2 - 6(1) + 4 = -1 Substitute 1 fo r x and simplify.

W h e n x = l , y = — 1, s o a n o t h e r p o i n t is (1 , —1).

St e p 3 Graph the vertex and the points you found in

Step 2, (0,4) and (1, -1). Reflect the points

from Step 2 across the axis of symmetry to get

two more points on the graph. Then connect

the points with a parabola.

Go t I t? 1- a. What is the graph of the function y = - x 2 + 4x - 2?

b. Reasoning In Step 2 of Problem 1, why do you think it was useful to use

the y-intercept as one point on the graph?

554 Chapter 9 Quadratic Functions and Equations