Solving Quadratic Equations by the Quadratic Formula

1
Section 8.2

• Solving Quadratic Equations by the Quadratic
  Formula

2
The Quadratic Formula

• We now add another method for solving quadratic
  equations to our toolbox.
• Factoring (works with some quadratics)
• Square Root Property (works with some)
• And now, The Quadratic Formula
• Works with all quadratics.
• Why do we need multiple methods?
• Want to use the method that is easiest/fastest.
• Methods will reach the same solutions, though.

3
The Quadratic Formula

• When we have a quadratic equation in standard
  form,
• We can use the Quadratic Equation to solve the
  equation
• Note Be sure to identify a,b, and c first!

4
Tips for using the Quadratic Formula

• If your equation contains rational functions (or
  even fractions), multiply both sides by the LCD
  side.
• ALWAYS start by writing the equation in STANDARD
  FORM.

5
Examples
6
Modeling with the Quadratic Equation

• In a right triangle, one leg is 3 inches less
  than the other. If the length of the hypotenuse
  is 7 inches, find the exact length of each leg.