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Unit 3, Day Two: Solving
Quadratic Equations by Factoring
Objective: Solve quadratic
equations by factoring!
Assignment: Pg. 261-262: 6777 odd, 81, 83, 87, 93.
Honors: In addition to above,
complete 79 and 91.
A few more examples on special patterns: Difference
of Squares– You can use pattern rules or factoring fanatic
9 x2  16
16b2  c2
(a  b)2  c2
Perfect Square Trinomials – Another Pattern to Explore
a  2ab  b  (a  b)
2
a  2ab  b  (a  b)
2
2
2
2
2
Examples: Factor the Quadratic Expressions
p2  4 p  4
x2  6 x  9
4 x 2  12 x  9
25c 2  60c  36
Solving Quadratic Equations
• You can use factoring to solve certain
quadratic equations. If a quadratic equation
can be factored, then the equation can be
solved using the zero product property.
• Zero Product Property:
Let A and B be real numbers or algebraic
expressions. If AB=0, the A=0 or B=0
So how does this pertain to
Quadratic Equations?
• After you have factored, look at each factor
independently.
• Solve for “x” when each factor equals zero!
• For example: ( x  3)(3x  4)  0
 x  3  0
x3 0
x  3
 3x  4 
 0
3x  4  0
3x  4
4
x 
3
x
4
, 3
3
Example- Solving a Quadratic
Equation
Solve
8x2  6 x  5  0
5 x 2  13 x  6
Example: Using a Quadratic Equation as a Model
You have just planted a rectangular flower bed of red roses in a park near
your home. You want to plant a border of yellow roses around the flower
bed as shown. Since you bought the same number of red and yellow
roses, the areas of the border and the inner flower bed will be equal. What
should the width x of the border be?
Finding Zeros of Quadratic
Function
The solutions you find to a quadratic function
are also called the zeros of the function. For
example, if you factor an equation and get:
(2 x  3)( x  4)  0
The solutions and the zeros to the function are
3
and  4
2
Example: Finding the Zeros of a Quadratic Function
Find the zeros (or x-intercepts) of:
(What do we do to find x-intercept?)
y  x  x6
2
Set y = 0 and then factor and solve.
0  x2  x  6
Recap
So, the solutions to a quadratic
equation are called the zeros of the
function. The zeros of the function
are where the graph of the function
crosses the x-axis or the x-intercepts!
You do not need to copy this slide
Graphing a Quadratic Function
• Graph: y  x  x  6 from the previous
example on your calculators.
Does your result match the zeros
we found earlier?
2