Investigating Transformations With DESMOS
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1 MPM D0 Date: Investigating Transformations With DESMOS INVESTIGATION Part A: What if we add a constant to the x in y = x? 1. Use DESMOS to graph the following quadratic functions on the same grid. Graph each of the following equations in a different colour. Draw a sketch of each parabola in a different colour. Label each graph with its equation. Note that your sketches do not need to be exact, but ensure that you have the vertex correct. Tap on the vertex to determine its location if necessary. b) x 3 y c) 9 d) 4 e) 5 f) 8. Complete the chart below. of Opening (0, 0) x = 0 Up Shifts up 3 units Describe the effect that the values of k in the function k had on the graph of. 4. Match the following graphs to their equations, without using your calculator: 4 5 1
2 Part B: What if a constant is added to the x in y = x? 5. Use DESMOS to graph the following quadratic functions on the same grid. Note that you must use brackets when entering the equations! Draw sketches of each of the graphs using different colours. Label each graph with its equation. c) e) b) y ( x 7) d) f) y ( x 6) y ( x 4) 6. Complete the chart below. (0, 0) x = 0 Up y ( x 6) Shifts right 6 units y ( x 7) y ( x 4) 7. Describe the effect that the values of h in the function y ( x h) had on the graph of. 8. Match the following graphs to their equations, without using your calculator. y ( x ) y ( x 7) y ( x 5)
3 Part C: What if the x in y = x was multiplied by a positive constant? 9. Use DESMOS to graph the following quadratic functions on the same grid. Draw sketches of each of the graphs using different colours. Label each graph with its equation. c) e) b) y 4x d) y 1/ x 10. Complete the chart below. (0, 0) x = 0 Up Stretched by a factor of y 4x y 1/ x 11. Describe the effect that the values of a in the function y ax had on the graph of. 1. Match the following graphs to their equations, without using your calculator. y 3x y 5x y 1/3x y 1/10x
4 Part D: What if the x in y = x was multiplied by a negative constant? 13. Use the graphing calculator to graph the following quadratic functions on the same grid. Draw sketches of each of the graphs using different colours. Label each graph with its equation. c) e) b) d) f) y x y 1/ 4x y x 14. Complete the chart below. (0, 0) x = 0 Up y x Reflected in the x-axis y 1/ 4x y x 15. Describe the effect that the values of a in the function y ax had on the graph of. PART E: PARABOLAS IN STANDARD FORM ( y ax bx c ) 16. In the top left corner of DESMOS, tap on the 3 lines. Choose Parabolas: Standard Form, choose open graph. Move the sliders around and make observations about what each value does. Include how each value differs if it is negative or positive. Value y ax bx c Observation a b c
5 PART F: PARABOLAS IN VERTEX FORM ( y a( x h) k ) 17. In the top left corner of DESMOS, tap on the 3 lines. Choose Parabolas: Form, choose open graph. Move the sliders around and make observations about what each value does. Include how each value differs if it is negative or positive. Value y a( x h) k Observation a h k PART G: PARABOLAS IN FACTORED FORM ( y a x x )( x ) ) ( 1 x 18. In the top left corner of DESMOS, tap on the 3 lines. Choose Parabolas: Form, choose open graph. Move the sliders around and make observations about what each value does. Include how each value differs if it is negative or positive. Value y a( x x1 )( x x) Observation a X1 X 19. Which form of the equation was easiest to work with and why?
6 Part H: Describing Parabolas 0. Without using DESMOS, complete the following chart comparing the graph of the graphs below. to each of Maximum or Minimum? Max. or Min. Value (0, 0) x = 0 Up Minimum 0 (0, ) x = 0 Up Minimum 6 y ( x 3) y 3x y x y 1/ 3x y 1/ 6x y ( x ) y ( x 4) y ( x 6) y ( x 5) y ( x 8) y x y 1/ ( x 7) y 4( x 1) 6
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