Chapter 9 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Solving Quadratic Equations by the Square Root Property Solve equations of the form x 2 = k, where k > 0. Solve equations of the form ( ax + b ) 2 = k, where k > 0. Use formulas involving squared variables

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solving Quadratic Equations by the Square Root Property In Section 6.5, we solved quadratic equations by factoring. Since not all quadratic equations can easily be solved by factoring, we must develop other methods. Slide Recall that a quadratic equation is an equation that can be written in the form for real numbers a, b, and c, with a ≠ 0. We can solve the quadratic equation x 2 + 4x + 3 = 0 by factoring, using the zero-factor property.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve 2x 2 − 3x + 1 = 0 by factoring. Solving Quadratic Equations Using the Zero-Factor Property Slide Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Solve equations of the form x 2 = k, where k > 0. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley We can solve equations such as x 2 = 9 by factoring as follows. Slide Solve equations of the form x 2 = k, where k > 0. We might also have solved x 2 = 9 by noticing that x must be a number whose square is 9. Thus, or

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Solve equations of the form x 2 = k, where k > 0. (cont’d) This can be generalized as the square root property. If k is a positive number and if x 2 = k, then or The solution set is, which can be written (± is read “positive or negative” or “plus or minus.”) When we solve an equation, we must find all values of the variable that satisfy the equation. Therefore, we want both the positive and negative square roots of k.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Solve each equation. Write radicals in simplified form. Solution: Solving Quadratic Equations of the form x 2 = k Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Solve equations of the form (ax + b) 2 = k, where k > 0. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley In each equation in Example 2, the exponent 2 appeared with a single variable as its base. We can extend the square root property to solve equations in which the base is a binomial. Solve equations of the form (ax + b) 2 = k, where k > 0. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solve (p – 4) 2 = 3. EXAMPLE 2 Solving Quadratic Equations of the Form (x + b) 2 = k Slide Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Solution: Solving a Quadratic Equation of the Form (ax + b) 2 = k Slide Solve (5m + 1) 2 = 7.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Recognizing a Quadratic Equation with No Real Solutions Slide Solve (7z + 1) 2 = –1. Solution:

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Slide Use formulas involving squared variables.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Use the formula,, to approximate the length of a bass weighing 2.80 lb and having girth 11 in. Solution: Finding the Length of a Bass Slide The length of the bass is approximately in.