Page 602 - Algebra 1

y
c.
6
4
2
SOLUTION
f
(x)= x2 - 4x + 6
-4
-2
The graph does not cross the x-axis, so there are no x-intercepts, and therefore no real zeros.
An axis of symmetry is a line that divides a figure or graph into two mirror-image halves. All parabolas have an axis of symmetry that passes through the vertex of the parabola.
In the figure, notice that the equation of the axis of symmetry includes the x-coordinate of the vertex, 2. Also notice that 2 is the average of the zeros, 1 and 3.
y = 2x2 8x + 6
Example
3
Finding the Axis of Symmetry Using Zeros
Find the axis of symmetry for each graph.
a. b.
SOLUTION SOLUTION
Average the zeros to find the
Math Reasoning
Justify Why do the equations for the axes of symmetry begin with “x =” rather than “y =”?
(-4.5, 0)
y
(1,
2
0)
(3, 0) x
-2
-2
4
-4
(2, -2)
x
=
2
y
2
8
x
-6
-2
(-3,
0)
4
(5, 0)
x
-2
-8
-4
-4
-4
8
-6
When there is one zero, the zero _
occurs at the vertex point, so the vertex is at (-4.5, 0). Use the x-coordinate of the vertex to identify the axis of symmetry:
x = -4.5.
2
4
x
y
4
-8
x-coordinate of the vertex:
_
-3 + 5 = 2 = 1. The x-coordinate
22
of the vertex is 1. Since the axis
of symmetry passes through the vertex, the equation for the axis of symmetry is x = 1.
Lesson 89 587