4.4 Factoring Quadratic Expressions4.5 Quadratic Equations

I. VocabularyA. Factoring is rewriting an expression as a product of

its factors.B. Greatest Common Factor (GCF) of an expression is

a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent.

C. Perfect Square Trinomial is a trinomial that is the square of a binomial. Ex. x² + 6x + 9 = (x + 3)²

D. Difference of Two Squares is the expression a² - b², there is a pattern to its factors, (a-b)(a+b).

E. An expression or term that cannot be factored is considered to be prime.

II. Factor each expression completely.A. x² + 14 x + 40 B. –x² + 14x + 32

C. 7n² – 21 D. 4x² + 8x + 12

E. 4x² + 7x + 3 F. 2x² – 7x + 6

G. 64x² – 16x + 1 H. 25x² -81

I. 9x² + 16 J. 75x² - 27

4.5 Quadratic EquationsWherever the graph of a function f(x) intersects

the x-axis, f(x) = 0. a value of x for which f(x) is a zero of the function.

The Zero Product Property can be used to solve some quadratic equations in standard form.

If ab = 0 , the a=0 or b=0

I. Solve each equation by factoring.A. x² -7x = -12 B. 6x² + 4x = 0

II. Solving a Quadratic Equation with TablesWhat should we be looking for in the Calculator TABLE?

A. What are the solutions of the quadratic equation 4x² – 14x + 7 = 4 – x?

Step 1: Enter the equation in standard form as Y₁Step 2: Press 2nd Graph for TABLEStep 3: Locate where the y value is 0. If they are not

seen notice between what values they should be and make changes to TBLSET, so they can be displayed.

B. 4x² = x +3

III. Solving Quadratics by GraphingThink about what f(x) = 0, represents graphically. What are we looking for on the graph?

A. What are the solutions of the quadratic equation? 2x² + 7x -15 = 0

Step 1: Enter the equation in standard form as Y₁Step 2: Press 2nd Trace for CALCStep 3: Select Zero (so we can calculate when

f(x) = 0Step 4:Move cursor to select left and right

bound of intersection. Repeat for the second intersection.

B. ½ x² -x = 8

IV. Using the Quadratic EquationThe function y = -0.03x² + 1.60x models the path of a kicked soccer ball. The height is y, the distance is x, and the units are meters. How far does the soccer ball travel? How high does the soccer ball go? Describe a reasonable domain and range of the function.

Travels 53.3 metersHeight 21.3 meters

Homework Pre- AP p. 221 #59-69 odd, 83-87 oddp. 229 #9-21 odd, 36, 38, and 59