OBJECTIVE: STUDENTS WILL BE ABLE TO SOLVE A QUADRATIC EQUATION USING FACTORING AND THE ZERO PRODUCT PROPERTY 5.2: Part 2-Solving Quadratics by Factoring.

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Presentation transcript:

OBJECTIVE: STUDENTS WILL BE ABLE TO SOLVE A QUADRATIC EQUATION USING FACTORING AND THE ZERO PRODUCT PROPERTY 5.2: Part 2-Solving Quadratics by Factoring

When y=0, what part of the graph of any function are we finding??? Any quantity multiplied by 0 = ______.

Zero Product Property If a quadratic equation is in standard form, 0 = ax 2 + bx +c, and ax 2 + bx + c can be factored, then you can solve the equation using the zero product property. Prompting question….since 0 is put in the place of y, what are we really finding?

Zero Product Property If A·B = 0, then either A = 0 or B = 0 Applied to a quadratic equation: If (x –a)(x –b) = 0, then either x – a = 0 or x – b = 0 This allows us to solve for x in a quadratic equation.

Examples: Solve by factoring. 1. x 2 – 3x – 4 =0 What are the x-intercepts of the graph?

Examples: Solve by factoring. 1. x 2 + 2x =02. 5x 2 – 20 = 0

Solve the following by factoring. Why do these look different???!?!?! 1. 4y 2 – 4y = q 2 +4q -1 = 7q 2 -7q+1

Solve by Factoring 1. 9t = 12t

Zeros of a Function Intercept form of a quadratic: y = a(x-p)(x-q)  The x intercepts are the numbers p and q THE NUMBERS p AND q ARE CALLED THE ZEROS OF THE FUNCTION. WHY DO YOU THINK??

FIND THE ZEROS OF THE FUNCTIONS y= x 2 + 8x +15 Factor to write in intercept form: Set the equation = 0: Solve for x:

Example: Find the zeros. 1. y= x y=3x 2 +14x -5

Example A painter is making a rectangular canvas for her next painting. She wants the length of the canvas to be 4 ft more than twice the width of the canvas. The area of the canvas must be 30 ft 2. What should the dimensions of the canvas be?

Example, p. 258 You have made a rectangular stained glass window that is 2 ft by 4 ft. You have 7 sq. ft. of clear glass to create a border of uniform width around the window. What should the width of the border be?

Example The height of a rocket launched upward from a 160-ft cliff is modeled by y= -16t 2 +48t +160, where h is the height in feet and t is the time in seconds. When will the rocket hit ground level?