Page 603 - Algebra 1

The axis of symmetry can also be found by using a formula.
Axis of Symmetry Formula
The axis of symmetry for the graph of
a quadratic equation y = ax2 + bx + c
is x = -_b . 2a
6
4
2
y=ax2 +bx+c
x = - _b 2a
x
2
4
6
Math Reasoning
Analyze Describe the relationship between the vertex and the axis of symmetry.
Example
4
588 Saxon Algebra 1
Finding the Axis of Symmetry Using the Formula
Find the axis of symmetry for the graph of each quadratic function.
a. y = x2 + 6x + 5
SOLUTION
x = - _b
b. y = -2x2 + 3x - 1 SOLUTION
x = - _b
_2a
6 Substitute values.
_2a
3 Substitute values.
Simplify.
The equation of the axis of
symmetryisx=_3. 4
= -
= -3 Simplify.
= - = _3
2(1)
2(-2) 4
The equation of the axis of symmetry is x = -3.
Example
5
Application: Height of a Golf Ball
A golf ball is hit from an elevated platform 10 feet above the ground. It starts with a vertical speed of 160 feet per second. Ignoring friction, the equation y = -16t2 + 160t + 10 gives the height, y, as a function of time, t. Find the highest point the ball reaches and how long it takes to reach it.
SOLUTION Find t at the vertex by using the formula for the axis of symmetry.
t = -_b _2a
= - 160 2(-16)
= 5
Substitute 5 for t in the equation to find the y-value of the vertex. y = -16t2 + 160t + 10
= -16(5)2 + 160(5) + 10 Substitute 5 for t. = 410 Simplify.
The vertex is at (5, 410). This means that 5 seconds after the golf ball is hit, it reaches a maximum height of 410 feet.
axis of symmetry formula
Use a = -16 and b = 160.
Simplify.