1 P a g e Province Mathematics Department Southwest Tennessee Community College

Transcription

1 Chapter 10 Section Solving Quadratic Equations by the Square Root Property Objectives: 1. Review the zero-factor property. 2. Solve equations of the form x 2 = k, where k > Solve equations of the form (ax + b) 2 = k, where k > Solve quadratic equations with nonreal complex solutions. Review the zero-factor property 1 P a g e

2 Ex: Solve using the square root property. Ex: Solve using the square root property. Ex: Solve using the square root property 2 P a g e

3 Solve equations of the form (ax + b) 2 = k, where k > 0. Ex: Solve 2 ( x 3) 16. Ex: Solve 2 (2x 3) P a g e

4 Solve quadratic equations with nonreal complex solutions Ex: Solve Ex: 4 P a g e

5 Section Solving Quadratic Equations by the Quadratic Formula Objective: 1. Solve quadratic equations using the quadratic formula. 2 A quadratic equation in x can be written in the standard form bx c 0 where a, b, c, a 0. ax, Write the following problems in standard form and identify the values for a, b and c. Ex: Ex: Ex: 5 P a g e

6 Ex: Ex: Ex. Solve 6 P a g e

7 Ex. Solve Ex. Solve 7 P a g e

8 Section Formulas and Further Applications Objectives: 1. Solve applied problems using area formulas. 2. Solve applied problems using quadratic functions as models. Solving an Area Problem A gardener wants to make a flower bed of uniform width around a reflecting pool. The pool is 10 ft by 6 ft. The gardener has enough plants to cover 36 square feet. How wide should the border be? 8 P a g e

9 Solving Applied Problems Using a Quadratic Function A toy rocket is fired upward from the ground. The height h, in feet, of the rocket is given by h(t) = 80t -16t 2 where t represents time in seconds. Find the time it takes the rocket to reach a height of 48 feet, 9 P a g e

10 Section Graphs of Quadratic Functions Objectives: 1. Graph a quadratic function. 2. Graph parabolas with horizontal and vertical shifts. 3. Use the coefficient of x 2 to predict the shape and direction in which a parabola opens. 4. Find a quadratic function to model data. 10 P a g e

11 Vertical Translation (or Shift): For b > 0 : The graph of is the graph of shifted up b units For b < 0 : The graph of is the graph of shifted down b units Example Given that plot and 11 P a g e

12 Horizontal Translation(or Shift): For d > 0 : The graph of is the graph of shifted left d units For d < 0 : The graph of is the graph of shifted right d units Example Given that plot and 12 P a g e

13 Compound Example Given that and plot 13 P a g e

14 Ex: Describe the characteristics of the graph of 14 P a g e

15 Finding a Quadratic Model The following table shows the higher-order multiple birth rates in the United States since At the right is a scatter diagram of these points. 15 P a g e

16 Section More About Parabolas and Their Applications Objectives: 1. Find the vertex of a vertical parabola. 2. Graph a quadratic function. Find the Vertex of a Parabola Ex: Find the vertex of the graph of 16 P a g e

17 Ex: Find the vertex of the graph of 17 P a g e

18 Vertex Formula Ex: Find the vertex of 18 P a g e

19 Ex: Graph the quadratic function defined by 19 P a g e