USING TRANSFORMATIONS TO GRAPH QUADRATIC FUNCTIONS WORKSHEET

Write the equation for the function y = x² with the following transformations and draw the graph of it.

Problem 1 :

Reflect across the x-axis, shift down 1

Solution

Problem 2 :

Vertically stretch by a factor of 3, shift right 5 and up 1

Solution

Problem 3 :

If you wanted to shift

y = -3(x – 2)² + 1

down 4 and left 5 what would be the new equation?

Solution

Problem 4 :

If you wanted to shift y = x² + 3 left 2 and up 5 what would be the new equation?

Solution

Problem 5 :

If you wanted to shift y = (x + 4)² down 3 and right 2 what would be the new equation?

Solution

Problem 6 :

If you wanted to shift y = -x² right 3 and up 5 what would be the new equation?

Solution

Problem 7 :

Describe the following transformations on the function y = x²

y = (x + 3)² -1

Solution

Problem 8 :

Describe the following transformations on the function y = x²

y = -(1/2)(x - 1)² + 3

Solution

Problem 9 :

Describe the following transformations on the function y = x²

y = (1/3)(x + 2)² + 3

Solution

Answer Key

1)  y = -x² - 1

2) y = 3(x - 5)² + 1

3)  The required quadratic function is

y = -3(x + 3)² - 3

4) So, the required quadratic function is

y = (x + 2)² + 8

5)  So, the equation of the required quadratic function is 

y = (x + 2)² + 3

6)  So, the required equation is 

y = (x - 3)² + 5

7)  Horizontal shift of 3 units left and vertical shift of 1 unit down.

8)  Reflection across x -axis, vertical compression of 1/2 units, horizontal shift of 1 unit right and vertical shift of 3 units up.