Sect' 9'5 The Quadratic Formula

1
Sect. 9.5 The Quadratic Formula
Goal Solve Equations by Using the
Quadratic Formula
2
The Quadratic Formula
The quadratic equation
has the solutions
3
Quadratic Equations always include an x2. We have
several techniques to solve

• If of the form x2 c, we can take the
• square root of both sides and solve
  algebraically.
• We can write the related function and solve
• graphically (find the roots).
• 3. We can factor to solve (later chapter!)

The problem is that most quadratics can not be
factored, and graphing is not always convenient.
Therefore the Quadratic Formula is needed.
4
The Quadratic Formula solves equations

• Step 1 Arrange quadratic in standard form.
• Step 2 Write what a, b, and c are.
• Step 3 Plug the numbers into the formula.
• Step 4 Simplify especially the radical.
• Step 5 Write both answers.

5
Use the quadratic formula to solve the equation
4x2-4x-30
NOW JUST SOLVE
6
After plugging the numbers, into the equation, we
can separate the equation to solve for both x.
7
Solve
4 x2 3x

• Step 1 Arrange quadratic in standard form.

0 x2 3x 4
a 1, b 3, and c - 4

• Step 2 Write what a, b, and c are.

Step 3 Plug the numbers into the formula.
Step 4 Simplify especially the radical.

• Step 5 Write both answers.

Since the answers are rational, the original
problem would factor.
8
Solve Using Quadratic Formula
Solve x2 5x 6 0
9
Solve
3x2 - 15 6x
10
Solve
4x2 5 4x
11
Use the quadratic formula to solve the following
equation.
12
Use the quadratic formula to solve the following
equation.