Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Write and graph the standard equation of a parabola given sufficient information. Given an equation of a parabola, graph it and label the vertex, focus, and directrix. 9.2 Parabolas
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms axis of symmetry of a parabola directrix focus parabola vertex of a parabola 9.2 Parabolas
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Definition of a Parabola 9.2 Parabolas The graph of a quadratic function. The set of all points P(x, y) in the plane whose distance to a point, called the focus, equals the distance to a fixed line, called the directrix.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Standard Equation of a Parabola 9.2 Parabolas Horizontal Directrix: vertex: (0, 0) focus: (0, p) directrix: y = –p axis of symmetry: y-axis y = x 2 1 4p4p x y D(x, –p) P(x, y) F(0, p) y = –p O
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Standard Equation of a Parabola 9.2 Parabolas If p > 0, parabola opens upward. If p < 0, parabola opens downward. y = x 2 1 4p4p x y D(x, –p) P(x, y) F(0, p) y = –p O Horizontal Directrix:
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Standard Equation of a Parabola 9.2 Parabolas Vertical Directrix: vertex: (0, 0) focus: (p, 0) directrix: x = –p axis of symmetry: x-axis x = y 2 1 4p4p x y D(x, –p) P(x, y) F(p, 0) x = –p O
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Standard Equation of a Parabola 9.2 Parabolas If p > 0, parabola opens to the right. If p < 0, parabola opens to the left. x = y 2 1 4p4p Vertical Directrix: x y D(x, –p) P(x, y) F(p, 0) x = –p O
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Standard Equation of a Translated Parabola 9.2 Parabolas Horizontal Directrix: vertex: (h, k) focus: (h, k + p) directrix: y = k – p axis of symmetry: x = h y – k = (x – h) 2 1 4p4p
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Standard Equation of a Translated Parabola 9.2 Parabolas vertex: (h, k) focus: (h + p, k) directrix: x = h – p axis of symmetry: y = k Vertical Directrix: x – h = (y – k) 2 1 4p4p
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find the vertex, focus, and directrix of a parabola. Graph the parabola. 9.2 Parabolas 2y = x 2 – 2x + 7 standard form y – 3 = (x – 1) vertex: (1, 3) directrix: y = focus: (1, 3 ) TOC