1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate the axis of symmetry of a parabola. 5.5 The Quadratic Formula

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Term quadratic formula 5.5 The Quadratic Formula

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Quadratic Formula ax 2 + bx + c = 0, a  0 5.5 The Quadratic Formula roots : –b  b 2 – 4ac 2a2a

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Axis of Symmetry of a Parabola y = ax 2 + bx + c, a  0 5.5 The Quadratic Formula axis of symmetry:x = – b 2a2a

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Coordinates of Vertex of a Parabola ax 2 + bx + c = 0, a  0 5.5 The Quadratic Formula vertex: ( ) – b 2a2a b 2a2a f –f – ( ),

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the quadratic formula to find the real roots of quadratic equations. x 2 + 5x – 1 = 0 5.5 The Quadratic Formula a = 1, b = 5, c = –1 x  0.19 or x  –5.19 –b  b 2 – 4ac 2a2a 2(1) –5   5 2 – 4(1)(–1) 2 –5   29 TOC