y = x 2 b) Graph c) Summary x-intercepts
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1 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 Fill out the table summarizing your investigations from problems 1 thru 4. 1a) -intercepts 2a) -intercepts 3a) -intercepts 4a) -intercepts 1b) line of symmetry 2b) line of symmetry 3b) line of symmetry 4b) line of symmetry 1c) y-intercept 2c) y-intercept 3c) y-intercept 4c) y-intercept 1d) verte 2d) verte 3d) verte 4d) verte 5. Investigate. a) Table y y = 2 b) Graph c) Summary -intercepts line of symmetry y-intercept verte d) Look at the verte. As you move the right on the graph, describe the patter for how each point moves up. 6. Investigate y = ( 3) a) Table y b) Graph c) Summary -intercepts line of symmetry y-intercept verte d) The equation is in verte form. Look at the coordinates of the verte. What pattern do you see?
2 7. Investigate y = ( + 3)( 1). a) Table y b) Graph c) Summary -intercepts line of symmetry y-intercept verte d) The equation is in factored form. Look at the coordinates of the - intercepts. What pattern do you see? 8. Investigate y = a) Table y b) Graph c) Summary -intercepts line of symmetry y-intercept verte d) The equation is in standard form. Look at the coordinates of the y- intercept. What pattern do you see? Match the equation on the left with the information on the right. a. Verte form: y = ( 10) y-intercept (0, 9) b. Verte form: y = ( + 6) 2 8 c. Verte form: y = ( + 9) d. Factored form: y = ( 10)( 4) e. Factored form: y = ( + 9)( + 5) f. Factored form: y = ( + 6)( 2) g. Standard form: y = h. Standard form: y = i. Standard form: y = verte (10, 30) 11. -intercepts (10, 0) and (4, 0) 12. -intercepts (-6, 0) and (2, 0) 13. y-intercept (0, 10) 14. -intercepts (-9, 0) and (-5, 0) 15. verte (-9, 4) 16. verte (-6, -8) 17. y-intercept (0, -3)
3 Go to butenhoffmath.com and check out the algebra notes video: A 8-6 AStd5c: I can graph quadratic functions. AStd5b: I can solve quadratic equations using the Zero Product Property 1. Below is the graph of y = ( +1)( 3). What are the -intercepts? Zero Product Property: if ab=0 then a=0, b=0 or a=b=0 2. Solve for : 0 = ( +1)( 3) 3. Justify your answers from #2.
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5 A 8-6 Name BDFM? Why? AStd5c: I can graph quadratic functions. AStd5b: I can solve quadratic equations using the Zero Product Property 1. Below is the graph of. What are the -intercepts? 2. What is the Zero Product Property? y = ( + 5)( +1) 0 = ( + 5)( +1) 3. Solve for : 4. Justify your answers from #3. Solve for ( 4)( 12) = 0 ( +19)( 1) = 0 ( 7) = 0 ( + 2)( 3) = = = = =
6 13. Use the calculator steps below to graph and investigate. Go to butenhoffmath.com and check out the A 8-6 #13 video to see how to use the graphing calculator or a smart phone to graph. Table Graph TI-84+ Calculator steps for graphing 1. Press Y= 2. Type in ( + 2)( + 4) 3. Press GRAPH to see the graph 4. Press 2ND' and then GRAPH to see the table y y = ( + 2)( + 4) Summary -intercepts line of symmetry y-intercept verte 14. Graph and investigate y = TI-84+ Calculator steps for graphing 1. Press Y= 2. Type in Press GRAPH to see the graph 4. Press 2ND' and then GRAPH to see the table Table y Graph Summary -intercepts line of symmetry y-intercept verte 15. Find the points of intersection by graphing. a) b) " y = 2 5 # $ y = Solve for : ( + 3)( 2 4 5) = 0
7 Go to butenhoffmath.com and check out the algebra notes video: A 8-7 AStd5c: I can graph quadratic functions. AStd5b: I can solve quadratic equations using the Zero Product Property and the Quadratic Formula If 0 = a 2 + b + c = Then b ± b 2 4ac 2a Solve for. By factoring = 0 By using the quadratic formula. a= b= c=
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9 A 8-7 Name BDFM? Why? AStd5c: I can graph quadratic functions. AStd5b: I can solve quadratic equations using the Zero Product Property and the Quadratic Formula 1. Solve for. By factoring = 0 By using the quadratic formula. a= b= c= 2. Solve for. By factoring = 0 By using the quadratic formula. a= b= c= After studying the two quadratic equations, decide which strategy (factoring or quadratic formula) is best to try first. Write justifications for your choices to solve each problem using the method you chose = =
10 5. Use the calculator steps below to graph and investigate y = TI-84+ Calculator steps for graphing 1. Press Y= 2. Type in Press GRAPH to see the graph 4. Press 2ND' and then GRAPH to see the table Table y Graph Summary -intercepts line of symmetry y-intercept verte Match the equation on the left with the information on the right. a. Verte form: y = ( 7) y-intercept (0, 11) b. Verte form: y = ( + 9) 2 6 d. Factored form: y = ( +11)( 5) e. Factored form: y = ( 6)( + 2) g. Standard form: y = h. Standard form: y = verte (-9, -6) 8. -intercepts (6, 0) and (-2, 0) 9. y-intercept (0, -8) 10. verte (7, 14) 11. -intercepts (-11, 0) and (5, 0) 12. Eamine the parabola and the quadratic rules below. Determine which rule(s) is(are) the correct match for the graph. Justify your choice. For each rule that does not match, eplain how you know it doesn t. a. y = b. y = c. y = ( 1)( 8) d. y = ( +1)( +8) Solve for. 13. ( 4) 2 = ( +1) 2 = 5
11 Go to butenhoffmath.com and check out the algebra notes video: A 8-8 AStd5c: I can graph quadratic functions. AStd5b: I can solve quadratic equations using the Zero Product Property and the Quadratic Formula Solve for by either factoring or using the quadratic formula. Justify your method = = 0
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13 A 8-8 Name BDFM? Why? AStd5c: I can graph quadratic functions. AStd5b: I can solve quadratic equations using the Zero Product Property and the Quadratic Formula 1. Solve for = 0 By factoring By using the quadratic formula. a= b= c= After studying the two quadratic equations, decide which strategy (factoring or quadratic formula) is best to try first. Write justifications for your choices to solve each problem using the method you chose = = = = 0
14 6. Match the equation on the left with the information on the right. a. Verte form: y = ( +10) y-intercept (0, 6) b. Verte form: y = ( 4) 2 10 d. Factored form: y = ( +1)( 4) e. Factored form: y = ( 5)( + 4) g. Standard form: y = h. Standard form: y = verte (4, -10) 8. -intercepts (-1, 0) and (4, 0) 9. y-intercept (0, -13) 10. verte (-10, 4) 11. -intercepts (5, 0) and (-4, 0) 7. Eamine the parabola and the quadratic rules below. Determine which rule(s) is(are) the correct match for the graph. Justify your choice. For each rule that does not match, eplain how you know it doesn t. a. y = b. y = c. y = ( 1)( + 3) d. y = ( +1)( 3) 8. Celina was convinced she could write the equation for the table below. Gina wasn t so sure. Table y Celina said: I can get the equation quickly. a. How did Gina test Celina s equation? Show how she knows it is incorrect. All I have to do is use the -intercepts (-4, 0) and (2, 0) to create -4 0 the equation. The equation must be y=(+4)(-2) Solve for. Gina said: Not so fast! I tested your equation. It doesn t work. You need more math to get it right. b. Fi Celina s equation. Show or eplain how you did it. 9. ( + 2) 2 = ( 4) 2 =10
15 A 8-Review Part 2 Name BDFM? Why? 1. Write one complete sentence that describes what you learned this chapter. C-Level Solve for : 0 = by factoring. 3. by using the Quadratic Formula. 4. Investigate the equation: y = Table Graph y Summary -intercepts line of symmetry y-intercept verte B-Level Solve for : 0 = by factoring. 6. by using the Quadratic Formula.
16 7. Eamine the parabola and the quadratic rules below. Determine which rule(s) is(are) the correct match for the graph. Justify your choice. For each rule that does not match, eplain how you know it doesn t. a. y = b. y = c. y = ( 1)( + 3) d. y = ( +1)( 3) 8. Celina was convinced she could write the equation for the table below. Gina wasn t so sure. Table y Celina said: I can get the equation quickly. a. How did Gina test Celina s equation? Show how she knows it is incorrect. All I have to do is use the -intercepts (-5, 0) and (1, 0) to create -5 0 the equation. The equation must be y=(+5)(-1) Gina said: Not so fast! I tested your equation. It doesn t work. You need more math to get it right. b. Fi Celina s equation. Show or eplain how you did it. A-Level Solve for. 9. ( + 4) 2 = ( 4)( 2 3 4) = Investigate y =
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