# 10.5: Quadratic Equations by the Quadratic Formula

**At Grade**Created by: CK-12

## Learning Objectives

At the end of this lesson, students will be able to:

- Solve quadratic equations using the quadratic formula.
- Identify and choose methods for solving quadratic equations.
- Solve real-world problems using functions by completing the square.

## Vocabulary

Terms introduced in this lesson:

- quadratic formula
- roots, solutions to a quadratic equation

## Teaching Strategies and Tips

Emphasize that the quadratic formula comes from *completing the square* of a general quadratic equation.

- Point out that half the coefficient of
x squared can be found by*multiplying*by1/2 :

- Remind students to find common denominators before simplifying the right side of the equation.

Have students rewrite each quadratic equation in standard form first. See Example 3.

Use Example 4 to show students how one goes about choosing a solving method.

Teachers are encouraged to use quadratic equations with non-integer coefficients—decimals and fractions—as additional practice problems.

## Error Troubleshooting

General Tip: Some students may use the values of

- Remind students rewrite each quadratic equation in standard form first. See Example 3.

General Tip: Have students simplify one step at a time when using the quadratic formula:

- Substitute.
- Simplify under the radical.
- Determine the square root.
- Simplify the numerator.
- Simplify the denominator.
- Divide.

General Tip: Some common mistakes associated with the quadratic formula are:

- Not using the minus sign that goes with a coefficient.

Example:

- Losing the minus sign on
−b .

Example:

- Canceling a factor of the denominator with
−b only. Remind students that in order to cancel a factor from the denominator, it must be a common factor in every term in the numerator. Unless that factor comes out of the radical, then the factor in the denominator*cannot*be canceled.

Example: For

- Rounding at steps other than the last step.

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## Date Created:

Feb 22, 2012## Last Modified:

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