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4.4 Factoring Quadratic Expressions 4.5 Quadratic Equations

4.4 Factoring Quadratic Expressions 4.5 Quadratic Equations. Vocabulary Factoring is rewriting an expression as a product of its factors.

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4.4 Factoring Quadratic Expressions 4.5 Quadratic Equations

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  1. 4.4 Factoring Quadratic Expressions4.5 Quadratic Equations

  2. Vocabulary • Factoring is rewriting an expression as a product of its factors. • 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. • Perfect Square Trinomial is a trinomial that is the square of a binomial. Ex. x² + 6x + 9 = (x + 3)² • Difference of Two Squares is the expression a² - b², there is a pattern to its factors, (a-b)(a+b). • An expression or term that cannot be factored is considered to be prime.

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

  4. C. 7n² – 21 D. 4x² + 8x + 12

  5. E. 4x² + 7x + 3 F. 2x² – 7x + 6

  6. G. 64x² – 16x + 1 H. 25x² -81

  7. I. 9x² + 16 J. 75x² - 27

  8. 4.5 Quadratic Equations Wherever 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

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

  10. II. Solving a Quadratic Equation with Tables What 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 Y₁ Step 2: Press 2nd Graph for TABLE Step 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.

  11. B. 4x² = x +3 III. Solving Quadratics by Graphing Think about what f(x) = 0, represents graphically. What are we looking for on the graph?

  12. A. What are the solutions of the quadratic equation? 2x² + 7x -15 = 0 Step 1: Enter the equation in standard form as Y₁ Step 2: Press 2nd Trace for CALC Step 3: Select Zero (so we can calculate when f(x) = 0 Step 4:Move cursor to select left and right bound of intersection. Repeat for the second intersection. B. ½ x² -x = 8

  13. IV. Using the Quadratic Equation The 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 meters Height 21.3 meters

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

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