Section 9.1 Quadratic Functions and Their Graphs.

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Presentation transcript:

Section 9.1 Quadratic Functions and Their Graphs

OBJECTIVES A Graph a parabola of the form.

OBJECTIVES B Graph a parabola of the form.

OBJECTIVES C Graph a parabola of the form.

OBJECTIVES D Graph parabolas that are not functions of the form

OBJECTIVES 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

Practice Test Exercise #1 Chapter 9 Section 9.1A

Opens down.

Section 9.2 Circles and Ellipses

OBJECTIVES A Find the distance between two points.

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

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

OBJECTIVES 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)

Practice Test Exercise #9 Chapter 9 Section 9.2B

Practice Test Exercise #10 Chapter 9 Section 9.2C

Section 9.3 Hyperbolas and Identification of Conics

OBJECTIVES A Graph hyperbolas.

OBJECTIVES 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 )

Practice Test Exercise #16 Chapter 9 Section 9.3A

a = 3, b = 5

Section 9.4 Nonlinear Systems of Equations

OBJECTIVES A Solve a nonlinear system by substitution.

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

OBJECTIVES C Solve applications involving nonlinear systems.

Practice Test Exercise #18 Chapter 9 Section 9.4A

Use the substitution method to solve the system.

Section 9.5 Nonlinear Systems of Inequalities

OBJECTIVES A Graph second-degree inequalities.

OBJECTIVES B Graph the solution set of a system of nonlinear inequalities.

PROCEDURE 1. Graph each of the inequalities on the same set of axes. Graphing Nonlinear Inequalities

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

Practice Test Exercise #22 Chapter 9 Section 9.5A

Vertex: (0, –1) x y 1 – 2 –1 – 2