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Graph of Quadratic Functions of the Form

Graph of Quadratic Functions of the Form. f(x) = + (x-h) 2 + k. Prepared by:. Ansiluz H. Betco. San Bartolome High School. Objectives:. At the end of the lesson, students should be able to : draw the graph of Quadratic Function of the form f(x) = + (x-h) 2 + k using sketch pad

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Graph of Quadratic Functions of the Form

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  1. Graph of Quadratic Functions of the Form f(x) = + (x-h)2 + k Prepared by: Ansiluz H. Betco San Bartolome High School

  2. Objectives: At the end of the lesson, students should be able to : • draw the graph of Quadratic Function of the form f(x) = + (x-h)2 + k using sketch pad • observe the effects of changes in h and k in the graph of Quadratic Function • Sketch the graph of quadratic functions applying its properties.

  3. Target group : Secondary 3A • Duration : 50 minutes • Mode : Student centered/group work

  4. Do you know that a stream of water that is projected into the air forms a beautiful symmetrical curve? The curve is the graph of Quadratic Function Discovering Mathematics 2A

  5. ReviewIdentify the following parts pointed by arrows Maximum point Line of symmetry Line of symmetry Minimum point http://jwilson.coe.uga.edu/

  6. Sketch the graphs of the following functions on the same plane using Graphmatica. Group Activity 1 • y = x2 • y = x2 - 3 • y = (x-3)2 + 2 • y = (x+5)2 –2 Procedures on how to use Graphmatica Software Answer Next

  7. Procedure on how to useGraphmatica • Go to graphmatica interactive software. Enter y=x^2 in the function input area and then click enter. The graph of y = x2 will appear on the sketch area with grid lines. • Similarly, draw the graphs of y = x2 - 3, y = (x – 3)2 + 2 and y = ( x+ 5)2 – 2 on the same coordinate plane. • Study the graphs, copy and complete the following table. Then consider the graph of y = (x – h)2 + k, where h and k are constants Back

  8. Answer to Activity 1 y = (x-3)2 +2 y = x2 y= (x+5)2 - 2 y = x2 -3 Back Next

  9. Group Work Complete the following table (0 , -3) Minimum x = 0 Minimum x = 3 (3 , 2 ) Minimum (-5, -2) x = -5 Minimum (h, k) x = h

  10. Sketch the graphs of the following functions on the same plane using Graphmatica. Group Activity 2 • y = - x2 • y= -(x + 6)2 • y = -(x+3)2 + 3 • y = -(x-4)2 – 2 Answer Next

  11. Answer to Activity 2 y = (x+3)2 +3 y = -x2 y = -(x-4)2-2 y = -(x+6)2 Back Next

  12. Group Work Complete the following table . x = 0 Maximum (0 , 7) Maximum x = -3 (-3, 4) (4, -1) Maximum x = 4 (h, k ) x = h Maximum

  13. Complete the table by writing your observation It has the same Shape as the graph of y= x2 It has the same Shape as the Graph of y = - x2 It opens downward It opens upward Its minimum pt. Is at the point (h,k) Its maximum pt. Is at the pt. (h,k ) The line x=h is its Line of symmetry The line x = h is its line of symmetry (Discovering Mathematics 3A)

  14. y = (x-1)2 +2 1)Sketch the graph of y = (x-1)2 +2 without using Graphmatica Solution: First we gather some information before sketching the graph y = (x-h)2+k 1 , 2 Minimum point vertex ) ( h,k Now sketch the graph when x = o y = (0 – 1)2 + 2 = 3 ( 0 , 3 )

  15. 1)Sketch the graph of y = (x-1)2 +2 without using Graphmatica 2)Do the graph of y = -(x+4)2 +2 on the same plane. y = -(x+ 4)2+2 y = (x-1)2 +2 y = - (x - h) 2 + k follow the same solution ,2 - 4 Maximum point ( ) vertex h , k Now sketch the graph if x = -2 y = - ( -2 + 4)2 +2 = -2 ( - 2, -2 )

  16. 2)Do the graph of y = -(x+4)2 +2 on the same plane. Graph of y = + ( x – h )2 + k y = (x-1)2 +2 y = - (x +4 ) + 2

  17. any questions ?

  18. Let’s practice Sketch the graph of the following functions 1) y = ( x-2)2 + 5 2) f(x) = -( x+7)2 + 3 3) g(x) = ( x-5)2 - 1 4) h(x) = -( x-2)2 + 5 5) p(x) = ( x+ 3)2 – 3/2

  19. Answer to exercises h(x) = (x-2)2+5 p(x)=(x+3)2 -3/2 g(x) = (x-5)2 -1 h(x) = -(x-2)2+5 f(x)= -(x+7)2 +3

  20. Home work Determined the function whose graphs are describe below • The graph of f(x) = x2 shifted 3 units upward • The graph of g(x)= -42 shifted 6 units below the origin • The graph of h(x)=1/4 x2 shifted 2 units above the x-axis • The graph of p(x)=-3x2 shifted ½ unit to the right • The graph of d(x)= 2x2 shifted 7 units to the left

  21. References: • Mathematics 3A by Chow Wai Keung • Graphmatica online interactive software

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