Section 9 1 Quadratic Functions and Their Graphs

Section 9. 1 Quadratic Functions and Their Graphs

OBJECTIV ES A Graph a parabola of the form.

OBJECTIV ES B Graph a parabola of the form.

OBJECTIV ES C Graph a parabola of the form.

OBJECTIV ES D Graph parabolas that are not functions of the form

OBJECTIV ES E Solve applications involving parabolas.

PROPERTIES For Parabola The vertex is at the origin and the y-axis is its line of symmetry.

PROPERTIES For Parabola If a is positive, the parabola opens upward, if a is negative, the parabola opens downward.

PROPERTIES For Parabola

PROPERTIES For Parabola

PROPERTIES For Parabola

PROPERTIES For Parabola

Chapter 9 Section 9. 1 A Practice Test Exercise #1

Opens down.

Section 9. 2 Circles and Ellipses

OBJECTIV ES A Find the distance between two points.

OBJECTIV ES B Find the equation of a circle with a given center and radius.

OBJECTIV ES C Find the center and radius and sketch the graph of a circle when its equation is given.

OBJECTIV ES D Graph an ellipse when its equation is given.

DEFINITION The Distance Formula

RULE Graphing Equation of a Circle

RULE

Graphing Equation of an Ellipse Centered at (0, 0) If a and b are equal, the ellipse is a circle.

Graphing Equation of an Ellipse Centered at (h, k)

Chapter 9 Section 9. 2 B Practice Test Exercise #9

Chapter 9 Section 9. 2 C Practice Test Exercise #10

Section 9. 3 Hyperbolas and Identification of Conics

OBJECTIV ES A Graph hyperbolas.

OBJECTIV ES B Identify conic sections by examining their equations.

RULES Graphing Equation of a Hyperbola with Center at (0, 0)

RULES Graphing Equation of a Hyperbola with Center at (0, 0)

Graphing Equation of a Hyperbola with Center at (h, k)

Chapter 9 Section 9. 3 A Practice Test Exercise #16

Section 9. 4 Nonlinear Systems of Equations

OBJECTIV ES A Solve a nonlinear system by substitution.

OBJECTIV ES B Solve a system with two second-degree equations by elimination.

OBJECTIV ES C Solve applications involving nonlinear systems.

Chapter 9 Section 9. 4 A Practice Test Exercise #18

Use the substitution method to solve the system.

Use the substitution method to solve the system.

Use the substitution method to solve the system.

Section 9. 5 Nonlinear Systems of Inequalities

OBJECTIV ES A Graph seconddegree inequalities.

OBJECTIV ES B Graph the solution set of a system of nonlinear inequalities.

PROCEDURE Graphing Nonlinear Inequalit 1. Graph each of the 2. inequalities on the sam 3. set of axes.

PROCEDURE Graphing Nonlinear Inequalit 2. Find the region common to both graphs. The result is the solution set

Chapter 9 Section 9. 5 A Practice Test Exercise #22

Vertex: (0, – 1) x y 1 – 2 – 1 – 2