Transformations on Mother Parabola II PDF
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This document includes an example of transformations of the mother parabolas y=x^2. It demonstrates and shows how a positive number (not 1 or -1) in front of the x^2 changes the graph. In particular, the graph becomes narrower (stretch) when the number is greater than 1 and wider (compression) when it's less than 1.
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Transformations on Mother Parabola II Remember that having a negative sign in front of x2 causes a reflection in the xaxis; a mirror image and changes the graph from having a minimum to a maximum value for y. (3,9)...
Transformations on Mother Parabola II Remember that having a negative sign in front of x2 causes a reflection in the xaxis; a mirror image and changes the graph from having a minimum to a maximum value for y. (3,9) (−3,9) (−2,4) (2,4) (−1,1) (1,1) (0,0) (−1,−1) (1,−1) (−2,−4) (2,−4) (−3,−9) (3,−9) What happens when a number (that isn't 1 or 1) is in front of x2? Desmos Change the scale so the y's go from 25 to 25 Use Desmos to graph both y=x2 and y=3x2 on the same grid and copy and label the graphs on the grid below using different colours. How did the graph change from Mother Parabola?. Fill in the table of values for each equation. x 3 2 1 0 1 2 3 y=x2 y x 3 2 1 0 1 2 3 y=3x2 y What do you notice about the corresponding y values with the same x? What do you think would happen to the y values for y=2x2 and how would that graph compare to the other two graphs? Try it on Desmos and copy it to the grid above, using a different colour. On Desmos, delete y=2x2 and y=3x2, keeping y=x2 on the grid. As well, change the grid to 10 to 10 on the y scale. Now, graph the equation and copy and label both graphs on the grid below. How did the graph change compared to Mother Parabola? Fill in the table of values for each equation. x 3 2 1 0 1 2 3 y x 3 2 1 0 1 2 3 y What do you notice about the corresponding y values with the same x? What do you think would happen to the y values for and how would that graph compare to the other two graphs? Try it on Desmos and copy it to the grid above, using a different colour.. Summary: If the value in front of x2 is BIGGER than 1(regardless if it +ve or ve), it causes a VERTICAL STRETCH and makes the parabola narrower If the value in front of x2 is LESS than 1 (regardless if it +ve or ve), it causes a VERTICAL COMPRESSION and makes the parabola wider What about Ex.#1 State whether the parabola would open up or down and is stretched or compressed. Then determine the coordinates of the new point given. a) y=4x2, old point (2,4) b) y=0.25x2, old point (−3,9) c) old point (1,1) d) y=1.5x2, old point (0,0) Ex.#2 Describe the transformation and state its equation. HOMEWORK: p.178 #1,4abeh,8,1113, 14 use Desmos to help
