1. Using the Zero-Product Property to Solve a Quadratic

2. x–Intercepts, Solutions, Roots, and Zeros in Quadratics
x-intercept(s): Where the graph of y=ax2+bx+c crosses the x-axis. The value(s) for x that makes a quadratic equal 0.
Solution(s) OR Roots: The value(s) of x that satisfies 0=ax2+bx+c.
Zeros: The value(s) of x that make ax2+bx+c equal 0.

3. Zero Product Property If a . b = 0, then a and or b is equal to 0
Ex: Solve the following equation below.
0 = ( x + 14 )( 6x + 1 ) OR
Would you rather solve the equation above or this: 0 = x2 + 25x + 14 ?

4. Solving a Quadratic: Factoring
Solve:
Product c
(2x2)(-12)
-24x2
Factor to rewrite as a product 4 8x
-3x
-12
ax2c
8x x
GCF
2x2 x
___ bx
ax2 5x
Use the Zero-Product Property 2x -3
Sum

5. Solving a Quadratic: Already Factored
Solve:
The equation is already factored AND it equals 0. Half the work is already done. Just use the Zero-Product Property

6. Solving a Quadratic: Making Sure to Isolate 0
Solve:
Factor to rewrite as a product
Product c
(2x2)(-12)
420x2 5
Solve for 0 first!
30x
14x 35
ax2c
12x2 2x
30x x
GCF
___
ax2 bx 6x 7
44x
Use the Zero-Product Property
Sum

7. Solving a Quadratic: Make Sure to Isolate 0
Solve:
Factor to rewrite as a product
Product c
(x2)(-4)
-4x2 -4
Solve for 0 first!
-4x x -4
Distribute
ax2c x2 x
-4x x
GCF
___
ax2 bx x 1
-3x
Use the Zero-Product Property
Sum

8. Do we Need Another Method?
Use the Zero Product Property to find the roots of:
Product
But this parabola has two zeros.
(x2)(-7)
-7x2 c -7
ax2c
IMPOSSIBLE x2 bx
___
ax2
-3x
Sum
Just because a quadratic is not factorable, does not mean it does not have roots. Thus, there is a need for a new algebraic method to find these roots.