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Homework Review

Learn how to factor quadratic functions and determine their zeros. Practice completing the square to solve quadratic equations. Understand that non-factorable quadratic functions can still have zeros.

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Homework Review

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  1. Homework Review

  2. Do Now: Level 1Factor each quadratic function and determine the zeros if possible a. f(x) = x2+ 5x + 4 b. f(x) = x2 - 4x + 2 4 (x + 1)(x + 4) = 0 2 Not Factorable 1 4   x + 1 = 0 5 -4 x =-1 c. Approximate √10 x + 4 = 0 x = -4 3.2

  3. Do Now: Level 2 d. f(x) = 2x2 + 10x + 4 e. f(x) = 3x2- 12x - 15 f(x) = 2(x2 + 5x + 2) f(x) = 3(x2-4x – 5) -5 (x - 5)(x + 1) = 0 2 -5 1 x - 5 = 0   -4 5 x = 5 x + 1 = 0 Not Factorable x = - 1

  4. Do Now Level 2 f. Approximate √40 6.4

  5. 13.7 Completing the Square SWBAT solve quadratic equations by completing the perfect square Trinomial.

  6. If you cannot factor a quadratic function, does that mean it does not have zeros? Explain No.​The​functions​in​parts​(b)​and​(c)​cannot​be​factored​because​no​factors​of​the​ “c” value​can​add to get the “b” value. The functions might have zeros.

  7. GRAPH AND SEE b. f(x) = x2 - 4x + 2

  8. GRAPH AND SEE d. f(x) = x2+ 5x + 2

  9. Factor Perfect Square Trinomials Perfect Square Trinomial: Perfect Square Trinomials have first and last terms that are positive perfect squares. And the middle term is twice the product of the square roots of the first and third terms. x2 + 4x + 4 4 (x + 2)(x + 2) 2 2 4 (x + 2)2

  10. Factor Perfect Square Trinomials n2 + 8n + 16 16 (n + 4)(n + 4) 4 4 8 (n + 4)2

  11. Solving by Factoring Perfect Square Trinomials exact approximate (x+2)(x+2)=5 (n+4)(n+4)=6 16 4 (x+2)2 =5 (n+4)2 =6 4 4 2 2 √(x+2)2 =±√5 √(n+4)2 =±√6 4 8 x+2 =±√5 n+4 =±√6 x = -2 ±√5 n = -4 ±√6 n = -4 +√6 n = -4 -√6 n = -4 +2.5 n = -4 - 2.5 n = - 6.5 n = -1.5

  12. Factor and Solve Perfect Square Trinomials 81 25 (g+9)(g+9)=17 (p-5)(p-5)=9 9 -5 9 -5 (g+9)2 =17 (p-5)2 =9 18 -10 √(g+9)2 =±√17 √(p-5)2 =±√9 g+9 =±√17 p-5 =±3 g = -9 ±√17 p = 5 ±3 g = -9 -√17 g = -9 +√17 p = 5 +3 p = 5 -3 g = -9 – 4.2 g = -9 +4.2 p = 8 p = 2 g = - 13.2 g = -4.8

  13. Before factoring, how can you tell if a trinomial is a square trinomial? • Before factoring, I can tell if a trinomial is a square trinomial by checking for: • First term is a positive perfect square • Last term is a positive perfect square • The middle term is twice the product of the square root of the first term and the square root of the third term. What should a square trinomial look like when factored? After factoring the trinomial you should have the same factors. This means that you will have the same quantity squared.

  14. COMPLETING THE PERFECT SQUARE “TRINOMIAL” If a ≠ 1, divide each term by that value to create a = 1 x2 - 4x + 2 = 0 - 2 -2 Move the constant to the right hand side by adding or subtracting x2 - 4x = -2 Complete the square trinomial: x2 - 4x + 4 = -2 +4 Find and add it to both sides in order to complete the square and balance the equation

  15. COMPLETING THE SQUARE “TRINOMIAL” x2 - 4x + 4 = 2 Factor the square trinomial. (x–2)(x – 2)= 2 (x – 2)2= 2 Square root both sides (don’t forget the +/-) Simplify and solve

  16. COMPLETING THE SQUARE “TRINOMIAL” • Completing the square: • Check if a=1, if its not, divide each term by a. • Move the constant to the right. • Complete the Perfect Square by finding (b/2)2 and adding it to both sides of the equal sign. • Solve the completed square: • Factor the Perfect Square Trinomial. • Square root both sides • Simplify and solve x2 - 6x + 6 = 0 x2 - 6x = -6 x2 - 6x + 9 = -6 + 9 x2 - 6x + 9 = 3 (x - 3)2 = 3 √(x - 3)2 = ±√3 x – 3 = ±√3 x = 3 ± √3

  17. COMPLETING THE SQUARE “TRINOMIAL” 5x2 - 35x -40 = 0 • Completing the square: • Check if a=1, if its not, divide each term by a. • Move the constant to the right. • Complete the Perfect Square by finding (b/2)2 and adding it to both sides of the equal sign. • Solve the completed square: • Factor the Perfect Square Trinomial. • Square root both sides • Simplify and solve x2 - 7x -8 = 0 x2 - 7x = 8 x2 - 7x + 12.25 = 8+12.25 x2 - 6x + 12.25 = 20.25 (x – 3.5)2 = 20.25 √(x – 3.5)2 = ±√20.25 x – 3.5 = ±√20.25 x = 3.5 ± √20.25

  18. Must complete: you choose order Braingenie.ck12.org- Completing the Square Skills Practice (#1-6) 13.7 Exit Slip on engradela.org

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