Warm Up
Solve
x2 - 3x - 28 = 0
9.2 Solving Quadratic Equations by Graphing
Objectives
1. Solve quadratic equations by
graphing.
2. Estimate solutions of quadratic
equations by graphing.
Example 1: Two roots
Solve x2 - 2x - 8 = 0 by graphing.
axis:
vertex:
y­intercept:
other points:
SOLUTIONS: _________________
CHECK:
(By factoring)
Example 2: One root
Solve x2 - 6x + 9 = 0 by graphing.
axis:
vertex:
y­intercept:
other points:
SOLUTIONS: _________________
CHECK:
(By factoring)
Example 3: No real roots
Solve x2 - 2x + 5 = 0 by graphing.
axis:
vertex:
y­intercept:
other points:
SOLUTIONS: _________________
CHECK:
(By factoring)
Example 4: Estimating Solutions
The real roots found so far have been integers. However, the roots of quadratic equations are usually NOT integers. In these cases, use estimation to approximate the roots of the equation.
Solve x2 + 6x + 6 = 0 by graphing.
SOLUTIONS: _____________
Example 5: Estimating Solutions to Applications
Solve -16t2 + 65t + 1 = 0 .
SOLUTIONS: _____________
You Try:
Solve x2 + 3x - 10 = 0 by graphing.
axis:
vertex:
y­intercept:
other points:
SOLUTIONS: _________________
CHECK:
(By factoring)
HW # 94
Worksheet 9.2