Page 51 - Math Course 3 (Book 1)

Quadratic Equations: Graphing

A Double Root Your Turn!

Example Two Roots

2
Solve x – 2x – 8 = 0 by graphing.
Solve x + 8x = –16 by graphing.
2
A. {–2, 4}
First, rewrite the equation so one side is equal to B. {2, –4}
zero.
C. {2, 4}
2
x + 8x = –16 Original equation D. {–2, –4}
2
x + 8x + 16 = –16 + 16 Add 16 to each side. f(x) = x – 2x – 8
2
2
x + 8x + 16 = 0 Simplify.
(x + 4)(x + 4) = 0 Factor. Answer

x + 4 = 0 or x + 4 = 0 Zero Product Property.

x = –4 x = –4

Answer The solution is –4.

A Double Root
2
Solve x + 2x = –1 by graphing.

A. {1}
B. {–1}
2
x + 8x = –8
C. {–1, 1}
2
D. Ø f(x)x + 2x + 1
No Real Roots
Example

2
Solve x + 2x + 3 = 0 by graphing. Answer
2
Graph the related function f(x) = x + 2x + 3.
x y
–3 6

–2 3
–1 2
2
f(x) = x + 2x +3
0 3
1 6

The graph has no x-intercept.
Answer Thus, there are no real number
solutions for the equation.
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