Download Solving Quadratic Equations

Solving Quadratic
Equations
Factoring and Square Root Method
Quadratic equations are the equations of
parabolas.
 The solutions to quadratic equations are the
places that the parabola crosses the x-axis.
 You will remember we call these many names:

◦ Roots
◦ Solutions
◦ Zeros

There are several ways to solve quadratic
equations:
◦
◦
◦
◦
Factoring
Square Root Method
Completing the Square
Quadratic Formula
Quadratic Equations

Remember all of the factoring from the
beginning of the year?
◦
◦
◦
◦

GCF
Swing and Divide
Reverse Foil
Difference of Two Squares
Now you get to use it!!!
◦
Factoring

Solve the equation:
◦ x2 + x – 20 = 0
What is the only way
to get x2?
◦ (x +
What are the rules for
the signs?
)(x -
)=0
◦ (x + 5)(x – 4) = 0
◦x+5=0
and
◦ x = -5 and x = 4
Factoring
x–4=0
What are the factors
of 20 that have a
difference of 1?
Set each factor equal
to “0” and solve for
“x”.

Solve this one:
◦ x2 + 6x + 5 = -4
◦ x2 + 6x + 9 = 0
◦ (x + 3)(x + 3) = 0
◦x+3=0
◦ x = -3
Factoring
To solve quadratic
equations, they must be
equal to “0”.
Now factor.
If the factors are the
same, then there is only
one answer.

Try a couple more…just to keep those skills
fresh! 

3x2 + 10x – 8 = 0

2x2 = 3x

9x2 = 24x – 16
Factoring
This is one of the easiest methods!
 It does help if you know some perfect
squares, but don’t worry you can use a
calculator.
 Use the Square Root Method when you
only have two terms; a squared term and
a number.

◦ x2 – 9 = 0
Square Root Method

Solve this:
◦ x2 – 16 = 0
◦ x2 = 16
◦ x = ±4
Move the “16” to the other
side.
Take the square root of both
sides.
You always get two answers,
positive and negative.
Don’t forget this part.
Students always do and they
miss points!!!
Square Root Method

Try again!
◦ 3x2 – 9 = 0
◦ 3x2 = 9
◦
x2
=3
◦ x=± 3
When using the square root
method, solve the equation
as you would any other
equation.
After you move the “9”,
divide by “3”, then take the
square root.
If the square root can be
simplified, go for it otherwise
a radical is fine.
Square Root Method

What about these?
◦ x2 + 4 = 0
 x2 = -4
 x = ±2𝜄
◦
x2
– 12 = 0
 x2 = 12
 x = ±2 3
◦ 3x2 – 2 = 0
 3x2 = 2
2
 x2 =
3
 x=±
2
3
 x=±
6
3
Sometimes the solutions
are imaginary numbers.
Sometimes the solutions
are radicals that have to
be simplified.
Sometimes the solutions
are fractions that have to
be rationalized.
Use all of the skills we
worked on the last two
days!!
Square Root Method
The homework tonight will tell you what
method to use.
 Don’t get stuck trying to simplify your
answers. We can practice that more in
class.
 If you are still struggling with factoring,
please come see me or download the
factoring app on your iPhone.

Quadratic Equations