CHAPTER 9 Quadratic Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 9.1Introduction to Quadratic Equations 9.2Solving Quadratic Equations by Completing the Square 9.3The Quadratic Formula 9.4Formulas 9.5Applications and Problem Solving 9.6Graphs of Quadratic Equations 9.7Functions

OBJECTIVES 9.3 The Quadratic Formula Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aSolve quadratic equations using the quadratic formula. bFind approximate solutions of quadratic equations using a calculator.

The solutions of ax 2 + bx + c = 0 are given by 9.3 The Quadratic Formula Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution We identify a, b, and c and substitute into the quadratic formula: 2x 2 + 9x – 5 = 0 a = 2, b = 9, c = –5 9.3 The Quadratic Formula a Solve quadratic equations using the quadratic formula. ASolve using the quadratic formula. 2x 2 + 9x – 5 = 0 (continued) Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE a = 2, b = 9, c = –5 9.3 The Quadratic Formula a Solve quadratic equations using the quadratic formula. ASolve using the quadratic formula. (continued) Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To solve a quadratic equation: 1. Check to see if it is in the form ax 2 = p or (x + c) 2 = d. If it is, use the principle of square roots as in Section If it is not in the form of (1), write it in standard form. ax2 + bx + c = 0 with a and b nonzero. 3. Then try factoring. 9.3 The Quadratic Formula Solving Quadratic Equations (continued) Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

To solve a quadratic equation: 4. If it is not possible to factor or if factoring seems difficult, use the quadratic formula. The solutions of a quadratic equation can always be found using the quadratic formula. They cannot always be found by factoring. (When the radicand b 2 – 4ac > 0, the equation has real-number solutions. When b 2 – 4ac < 0, the equation has no real-number solutions. 9.3 The Quadratic Formula Solving Quadratic Equations Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution We write w 2 = –12w + 4 in standard form, identify a, b, and c, and solve using the quadratic formula: 1w w – 4 = 0 a = 1, b = 12, c = –4 9.3 The Quadratic Formula a Solve quadratic equations using the quadratic formula. BSolve: w 2 = –12w + 4 (continued) Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution 9.3 The Quadratic Formula a Solve quadratic equations using the quadratic formula. BSolve: w 2 = –12w + 4 Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Since the radicand,  59 is negative, there are no real-number solutions. Solution a = 5, b =  1, c = The Quadratic Formula a Solve quadratic equations using the quadratic formula. C Solve: 5x 2  x + 3 = 0 Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

EXAMPLE Solution Using a calculator we have: 9.3 The Quadratic Formula b Find approximate solutions of quadratic equations using a calculator. DUse a calculator to approximate to the nearest tenth the solution to the expression Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.