Transcript Solving Quadratic Equations by Completing the Square

Solving Quadratic
Equations by the
Quadratic Formula
THE QUADRATIC FORMULA
1. When you solve using completing the square
on the general formula ax 2  bx  c  0
you get:
b  b2  4ac
x
2a
2. This is the quadratic formula!
3. Just identify a, b, and c then substitute into
the formula.
WHY USE THE
QUADRATIC FORMULA?
The quadratic formula allows you to solve
ANY quadratic equation, even if you
cannot factor it.
An important piece of the quadratic formula
is what’s under the radical:
b2 – 4ac
This piece is called the discriminant.
Example #1
Find the value of the discriminant and describe the nature of the
roots (real,imaginary, rational, irrational) of each quadratic
equation. Then solve the equation using the quadratic formula)
1.
2 x 2  7 x  11  0
Discriminant =
a=2, b=7, c=-11
b 2  4ac
(7) 2  4(2)( 11)
49  88
Discriminant = 137
Value of discriminant=137
Positive-NON perfect
square
Nature of the Roots –
2 Reals - Irrational
Example #1- continued
Solve using the Quadratic Formula
2 x 2  7 x  11  0
a  2, b  7, c  11
b  b 2  4ac
2a
7  7 2  4(2)(11)
2(2)
7  137
4
2 Reals - Irrational
Quadratic Formula

There once a negative boy who was all mixed
up so he went to this radical party. Because
the boy was square, he lost out on
4 awesome chicks so he cried his way home
when it was all over at 2 AM.
x
b 
b  4ac
2a
2
Solving Quadratic Equations
by the Quadratic Formula
Try the following examples. Do your work on your paper and then check
your answers.
1. x  2 x  63  0
2
2. x  8 x  84  0
2
3. x  5 x  24  0
2
4. x  7 x  13  0
2
5. 3 x 2 5 x  6  0
1.  9, 7 
2.(6, 14)
3.  3,8 
 7  i 3 
4. 

2


 5  i 47 
5. 

6

