The Quadratic Formula
The Quadratic Formula allows us to solve quadratic equations. It is
the most useful when trying to solve quadratics that cannot be
factored.
Given a quadratic equation in the form
√
NOTE: The values for
method.
and
are the same values we use for the
Example 1:
Solve for
if
Using the quadratic formula
1
√
(
)
)
√(
( )
We must follow the order of operations
√
√
We have two solutions:
and
2
( )(
)
Proof of the Quadratic Formula
Let
,
Given
Divided both sides by
(
)
(
)
(
)
(
(
(
(
(
(
Add ( ) to both sides
)
Complete the square (factor)
)
Subtract on both sides
)
Simplify exponents
)
Make like terms
)
Combine like terms
)
Square root both sides
√
Simplify denominator
√
√
Subtract
on both sides to isolate
Combine like terms
√
3
The Quadratic Formula
Practice Problems
Use the quadratic formula to solve each equation.
1.
2.
3.
4