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2.3 Quadratic Functions by Factoring

2.3 Quadratic Functions by Factoring. ACT.

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2.3 Quadratic Functions by Factoring

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  1. 2.3 Quadratic Functions by Factoring ACT

  2. F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* • A-CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* • Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. • A-REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* • F-IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima. • F-IF.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. • A-REI.4b: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Objectives

  3. Bell Ringer • Is a value of the input X that makes the output f(x) equal zero. • The zeros of a function are the x-intercepts What are the zeros of a function ? Memorize! • Zero-Product Property: • If ab = 0, then a = 0 or b = 0; Example: If (x + 3)(x-7) = 0, then (x + 3) = 0 or (x - 7) = 0. Suggestion Make poster

  4. Product of ac x +6x = -8 2 set = to 0 ? a = 1 ? x + 6x + 8 = 0 2 Add (S) Multiply (P) P S 1 8 9 Sum of a+b 6 (x + 2)(x + 4) 2 4 Sign! Solve by Factoring FOIL

  5. x + 3x = -2 set = to 0 ? 2 x + 3x + 2 = 0 2 a = 1 ? P S (x + 1)(x + 2) 1 2 3 zeros FACTORING

  6. x2 + 8x + 7x2 + 6x + 4 x2 + 12x + 32 Factor example(s) : your turn-use dry erase or note paper

  7. Factor x2 – 17x + 72 Reminder: find factors with product ac and a + b. ( - ) ( - ) Example... Changing the signs

  8. x2 – 7x + 12 x2 – 11x + 24 x2 – 14x - 32 Factoring examples, your turn

  9. x2 + 3x – 10 ( + ) ( - )

  10. x2 – 11x = - 15 • Write in standard form • Factor • Use the zero-product property • Solve for x Putting it all together

  11. Factor x2 – 5x - 6 • Factor x2 + 7x + 10 • Factor x2 – 3x + 2 Pick up Factoring worksheet; BEGIN! We work bell-to-bell Worksheet due next class Exit Question(s)

  12. x2 – 5x - 6 • x2 + 5x + 6 • x2 – 5x + 6 Bell Ringer Factor and apply Zero-Product Property Factoring with Technology

  13. In the next example, you must set the equation equal to zero before applying technology.

  14. To solve, simply set the individual factors equal to zero. The solutions are -3 and 1/2.

  15. Factoring : Perfect Squares Factor using “difference of two squares.” In this example, you must first factor the equation. Notice the familiar pattern. Notice sign

  16. 2 2 2 81x - 36 16x - 6561 4x + 25 Factoring : Perfect Squares with technology

  17. Compare these two functions: use a Venn Diagram 2 X– 9 = 0 X – 9 = 0 Exit Question

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