1. 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 : a) draw the graph of Quadratic Function of the form f(x) = + (x-h) 2 + k using sketch pad b) observe the effects of changes in h and k in the graph of Quadratic Function c) 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. Review Identify the following parts pointed by arrows Maximum point Minimum point Line of symmetry Line of symmetry http://jwilson.coe.uga.edu/

6. Sketch the graphs of the following functions on the same plane using Graphmatica. 1) y = x 2 2) y = x 2 - 3 3) y = (x-3) 2 + 2 4) y = (x+5) 2 –2 Procedures on how to use Graphmatica Software Answer Group Activity 1 Next

7. Procedure on how to use Graphmatica a) Go to graphmatica interactive software. Enter y=x^2 in the function input area and then click enter. The graph of y = x 2 will appear on the sketch area with grid lines. b) Similarly, draw the graphs of y = x 2 - 3, y = (x – 3) 2 + 2 and y = ( x+ 5) 2 – 2 on the same coordinate plane. c) 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. y= (x+5) 2 - 2 y = x 2 y = x 2 -3 y = (x-3) 2 +2 Answer to Activity 1 Back Next

9. Function Line of Symmetry Turning Point Is the turning point maximum or minimum? 1) y = x 2 x = 0(0, 0) Minimum 2) y = x 2 -3 3) y = (x-3) 2 + 2 4) y = (x+5) 2 – 2 5) y = (x-h) 2 + k Group Work Complete the following table x = 0 x = 3 x = -5 x = h (0, -3) (3, 2 ) (-5, -2) (h, k) Minimum

10. Sketch the graphs of the following functions on the same plane using Graphmatica. 1) y = - x 2 2) y= -(x + 6) 2 3) y = -(x+3) 2 + 3 4) y = -(x-4) 2 – 2 Answer Group Activity 2 Next

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

12. Function Line of Symmetry Turning Point Is the turning point maximum or minimum? 1) y =- x 2 x = 0( 0, 0)Maximum 2) y =- x 2 +7 3) y = - (x+3) 2 + 4 4) y= - (x - 4) 2 - 1 5) y = - (x-h) 2 + k Group Work Complete the following table. x = 0 x = -3 x = 4 x = h (0, 7) (-3, 4) (4, -1) (h, k ) Maximum

13. ObservationGraph of y = (x-h) 2 + k Graph of y = - (x-h) 2 + k 1) Compare the shape of the graphs 2) Opening of the graphs 3) Turning point of the graphs 4) The line of symmetry Complete the table by writing your observation It has the same Shape as the graph of y= x 2 It has the same Shape as the Graph of y = - x 2 It opens upward It opens downward 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. 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-1) 2 +2 y = (x-h) 2 +k ( ) h,k 1, 2 vertex Minimum point when x = o y = (0 – 1) 2 + 2 = 3 ( ) 0, 3 Now sketch the graph

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

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

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 g(x) = (x-5) 2 -1 h(x) = (x-2) 2 +5 h(x) = -(x-2) 2 +5 p(x)=(x+3) 2 -3/2 f(x)= -(x+7) 2 +3

20. Home work Determined the function whose graphs are describe below 1) The graph of f(x) = x 2 shifted 3 units upward 2) The graph of g(x)= -4 2 shifted 6 units below the origin 3) The graph of h(x)=1/4 x 2 shifted 2 units above the x-axis 4) The graph of p(x)=-3x 2 shifted ½ unit to the right 5) The graph of d(x)= 2x 2 shifted 7 units to the left

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