Chapter 4: Quadratic Functions and Equations

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Presentation transcript:

Chapter 4: Quadratic Functions and Equations Section 4.5: Quadratic Equations

Section 4.5: Quadratic Equations Goal: To solve quadratic equations by factoring and to solve quadratic equations by graphing

Section 4.5: Quadratic Equations Zero of the function: a value of x for which f (x) = 0 Wherever the graph of a function crosses the x-axis

Section 4.5: Quadratic Equations Zero Product Property: If ab = 0, then either a = 0 or b = 0 You can solve some quadratic equations in standard form by factoring the quadratic expression Examples: Find the solutions of the quadratic equation: x2 + 2x – 15 = 0

Section 4.5: Quadratic Equations Examples: 1. What are the solutions of the quadratic equation: x2 + 3x – 18 = 0 2. What are the solutions of the quadratic equation: 10x2 + 2x – 46 = x – 4

Section 4.5: Quadratic Equations Examples: 3. What are the solutions of the quadratic equation: 5x2 – 8 = 18x

Section 4.5: Quadratic Equations Using a Quadratic Equation The function f (x) = -0.002x2 + 0.77x models the path of a baseball, where f (x) gives the height of the ball and x gives the distance from where it is hit in feet. A) How far does the ball travel before hitting the ground? B) How high does the ball go? C) What is a reasonable domain and range for such a function?

Section 4.5: Quadratic Equations Examples: 4. The students in Mr. Wilson’s Physics class are making golf ball catapults. The flight of group A’s ball is modeled by the equation y = -0.014x2 + 0.68x, where x is the ball’s distance from the catapult. The units are in feet. A) How far did the ball fly? B) How high about the ground did the ball fly? C) What is the reasonable domain and range for this function?

Section 4.5: Quadratic Equations Homework: Pg. 229 #10-52 (even), #59