Download The Quadratic Formula

x 
a
b
1 , 4 , 9 , 16 , 25 , 36 , …
Simplify the following radicals.
1)
100
 10
2)
18

9
2
3 2
3)
28

4
7
2 7
4)
300

100 
3  10 3
20.02
Quadratic
Formula
Some quadratic equations ( ax2 + bx + c = 0 )
cannot be solved by factoring because the
polynomial cannot be factored.
We can still solve the equation by
using the Quadratic Formula.
Quadratic Formula
 b  b  4ac
x
2a
2
Quadratic Equation
ax  bx  c  0
2
Quadratic Formula
x
b
b  4ac
2a
2
To solve an equation using the Quadratic Formula
1) Identify a , b , c
2) Replace the variables in the
formula with these numbers.
3) Simplify
4) Write out the answers
( Don’t forget about the + )
Quadratic Equation
Quadratic Formula
ax 2  bx  c  0
Solve:
x
x 
b
b 2  4ac
2a
x2 + 8x + 15 = 0
 (8) 
(8) 2  4(1)(15)
2(1)
 8  64  60
x
2
8 2
x
2
x  3
Identify a , b , c
8

2
a = 1 , b = 8 , c = 15
4
8 2
8 2

or
2
2
or
x  5
Replace the
variables with
these numbers
Simplify
Write both
answers
Quadratic Equation
Quadratic Formula
ax 2  bx  c  0
Solve:
x
x
2x2 – 8x – 4 = 0
 (8) 
8
x 
b
8 4 6
x
4
x  2 
Identify a , b , c
(8) 2  4(2)( 4)
2(2)
64  32
4
6
a=2,b=–8,c=–4
 8  96

4
 2 
or
b 2  4ac
2a
6
x  2 
Replace the
variables with
these numbers
Simplify
Write both
answers
6
Quadratic Equation
Quadratic Formula
ax 2  bx  c  0
Solve:
x
x
b 2  4ac
2a
3x2 + 2x – 7 = 0
 (2) 
2
x 
b
(2) 2  4(3)( 7)
2(3)
4  84
6
 2  2 22
x
6
 1 22
x
3
 2  88

6
 1  22

3
or
 1  22
3
Quadratic Equation
Quadratic Formula
ax 2  bx  c  0
b 2  4ac
2a
x2 + 2x + 6 = 0
Solve:
x
x 
b
 (2) 
(2) 2  4(1)(6)
2(1)
4  24
 2   20
x

2
2
Can’t take the square root of a negative number
2
Therefore, there’s no solution.
or is there?
x  1  i 5