y = (x + 2)(x + 3) y = (2x + 3)(x 4) 15x x 2
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1 Go to butenhoffmath.com and check out the algebra notes video: A 8-1 AStd5a: I can rewrite quadratic equations in standard form, factored form, and vertex form. Factored form: y = (x + )(x + 3) y = (x + 3)(x 4) Vertex Form: y = (x 6) y = (x + 5) + x 30 x 15x Standard form:
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3 A 8-1 Name BDFM? Why? AStd5a: I can rewrite quadratic equations in standard form, factored form, and vertex form. 1. Factored form: y = (x + 6)(x + 7) y = (x +8)(x + 9) y = (4x +1)(x + ) Are the two forms of the quadratic equivalent? Justify your answer. y = (x 3)(x 10) and y = x 13x + 30 Standard form:. Write one complete sentence describing what the factored form of a quadratic looks like. 3. Factored form: y = (x +1)(x 5) y = (x 5)(x + 6) y = (x 5)(x + 9) Are the two forms of the quadratic equivalent? Justify your answer. y = (x 5)(x +1) and y = x 11x 5 Standard form: 4. Write one complete sentence describing what the standard form of a quadratic looks like. 5. Factored form: y = (x +1) y = (x 5) y = (x + 6) Are the two forms of the quadratic equivalent? Justify your answer. y = (x 5) and y = x 10x + 5 Standard form:
4 6. x 4 3x 9 9x 81 7x 49 x x x 3x x 9x x 7x Factored form: Standard form: x 6 x 14 3x 18 8x 7 x 3x x 7x x 6x x 9x 7. Vertex form: y = (x + ) + 5 VF: y = (x + 4) 7 VF: y = (x 7) +1 Are the two forms of the quadratic equivalent? Justify your answer. y = (x + 4) 5 and y = x +8x + 9 Standard form: 8. Write one complete sentence describing what the vertex form looks like. 9. x 5 3x 1 x 3 1x 0 x 10x x 8x x 6x 3x 5x
5 Go to butenhoffmath.com and check out the algebra notes video: A 8- AStd5a: I can rewrite quadratic equations in factored form given the standard form. Step 1 x +8x + 7 Step x +8x + 7 Step 3 Step 4 x +8x + 7 = Step 1 Step Step 3 Step 4 1. What are the factors of 1?. x + 7x +1 = 3. x +8x +1 = 4. x +13x +1 =
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7 A 8- Name BDFM? Why? AStd5a: I can rewrite quadratic equations in factored form given the standard form. 1. What are the factors of 16?. x +8x +16 = 3. x +10x +16 = 4. x +17x +16 = 5. What are the factors of 0? 6. x + 9x + 0 = 7. x +1x + 0 = 8. x + 1x + 0 = 9. What are the factors of 18? 10. x + 9x +18 = 11. x +11x +18 = 1. x +19x +18= 13. What are the factors of 4? x + 4 x = 15. x + 14x + 4 = x + 4 x = x + 4 x = 18. x + 3x 4 = x 4 x =
8 1. + 5x 4 x =. x + x 4= 3. 3x 4 x = 4. 10x 4 x = 5. x 5x 4 = 6. x 4 x = 7. Write an equation in the given form. a. Linear b. Factored form c. Standard form d. Vertex form Are the following pairs of quadratic equations equivalent? Justify your answer. 8. y = (x 3)(x + 4) and y = x + 7x 1 9. y = (x 6) and y = x y = (x + 4) 5 and y = x +8x Find the factored form and the standard form. x 4 3x 6 x 8 5x 0 3x 1x x 4x 3x 1x x 8x
9 Go to butenhoffmath.com and check out the algebra notes video: A 8-3 AStd5a: I can rewrite quadratic equations in vertex form given the standard form by completing the perfect square. Vertex form: y = (x + 3) 4 Convert this equation to standard form. Fill in the blank to complete the perfect square and write the factored/vertex form. Standard Form: y = x +1x + 7 Convert this equation to vertex form. x +1x + x +14x + Standard Form: y = x +14x 10 Convert this equation to vertex form.
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11 A 8-3 Name BDFM? Why? AStd5a: I can rewrite quadratic equations in vertex form given the standard form by completing the perfect square. 1. Fill in the blank to complete the perfect square and write the factored/vertex form x +18x + x + x + x 6x + x +8x + x + 4x + x + 9x +. Find the vertex form by completing the perfect square. Standard Form: y = x +18x + 3 Convert this equation to vertex form. Standard Form: y = x + x + 5 Convert this equation to vertex form. Standard Form: y = x 6x 1 Convert this equation to vertex form. Standard Form: y = x +8x +10 Convert this equation to vertex form. Standard Form: y = x + 4x 5 Convert this equation to vertex form. Standard Form: y = x + 9x + Convert this equation to vertex form. 3. Find all the factors of Find the factored form. a. y = x + 6x + 5 b. y = x + 4x 5 c. y = x 6x + 5 d. y = x 4x 5
12 5. Find the factored form (FF) and the standard form (SF). x 8 5x 30 15x 0 3x 18 3x 1x x 1x 3x 4x x 1x 6. Are the quadratic equations equivalent? Show by completing the square. y = x +8x + 5 y = x 10x + 6 and y = (x + 4) +10 and y = (x 5) +1 y = x +8x +16 and y = (x + 4) Convert y = x + 6x +8 to standard form, factored form and vertex form. Theresa wanted to solve ( x + x 10) = ( x ) and she knows that her final equation has to be set equal to zero. Here are her first two steps: 8. Help her finish rewriting the quadratic in standard form. ( x + x 10) = ( x ) 4( x + x 10) = x 4x + 4
13 Go to butenhoffmath.com and check out the algebra notes video: A 8-4 AStd5a: I can rewrite quadratic equations in factored form given the standard form. Step 1 3x + 7x + Step Step 3 Step 4 3x + 7x + 3x + 7x + Step 1 Step Step 3 Step 4 Factor. 1. 3x + 4x +1 =. 3x +10x + 3 = 3. 3x +13x + 4 =
14
15 A 8-4 Name BDFM? Why? AStd5a: I can rewrite quadratic equations in factored form given the standard form. Factor. 1. x + 3x +1 =. x + 5x + = 3. x + 7x + 3 = 4. x + 9x + 4 = 5. x +11x + 5 = 6. x + 4x + = 7. x + 5x + 3 = 8. x + 6x + 4 = 9. x +13x + 6 = 10. x 13x + 6 = 11. x 11x 6 = 1. x +11x 6 = Multiply 13. (x + 6x + 9) 14. 4(x x 6) 15. 5(x + x 15) Factor out. 16. x +1x x 4x x +10x 75
16 19. x + 4x + 0. x 16x x 9x 30. Refer back to #19. a. Find the factored form of #19 before you factored out. b. Find the factored form of #19 after you factored out. 3. Refer back to #0. a. Find the factored form of #0 before you factored out. b. Find the factored form of #0 after you factored out. 4. Refer back to #1. a. Find the factored form of #1 before you factored out. b. Find the factored form of #1 after you factored out. 5. Without factoringhich quadratic expressions below may have more than one factored form? Explain your reasoning. a. 3x 18x + 7 b. x 11x +111 c. 4x 1x 8 d. 3x + 3x 1
17 A 8-Review Name BDFM? Why? 1. Write one complete sentence that describes what you learned this chapter. C-Level Find the standard form. Factored form: y = (x + 6)(x + 7) 3. Factored form: y = (x 5)(x + 6) 4. Vertex form: y = (x + ) Vertex form: y = (x 7) +1 Find the factored form. 6. y = x +14x y = x 7x 8 B-Level Find the standard form. 8. Factored form: y = ( x + 6)( x + 7) 9. Factored form: y = ( 3x 5)( x + 6) Find the factored form. 10. Standard form: y = x + 7x Standard form: y = 3x + x 1. Find the vertex form. y = x + 6x +18
18 Are the two forms of the quadratic equivalent? Justify your answer. 13. y = (x + 3) and y = x y = (x + 4) 5 and y = x +8x + 9 Find the standard form. A-Level 15. Factor out a number to simplify 3x +18x Refer to #15. Find the factored form before you factored out and then find the factored form after you factored out. 17. Without factoring, which quadratic expressions below may have more than one factored form? Explain your reasoning. a. 3x 18x + 7 b. x 11x +111 c. 4x 1x 8 d. 3x + 3x 1 Theresa wanted to solve ( 5x + x 3) = ( x + 5) and she knows that her final equation has to be set equal to zero. Here are her first two steps: 18. Help her finish rewriting the quadratic in standard form. ( 5x + x 3) = ( x + 5) 4( 5x + x 3) = x + 5x + 5
y = x 2 b) Graph c) Summary x-intercepts
A 8-5 Name BDFM? Why? AStd5c: I can graph quadratic functions. Investigate the parabola. Circle the -intercepts, draw the line of symmetry, put a star net to the y-intercept, and put a v net to the verte.
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