Lesson on Transformations of the Quadratic Function

Lesson on Transformations of the Quadratic Function

Multiple Choice

How did we transform from the parent function?

y = x² + 2

• horizontal shift up

• vertical shift up

• horizontal shift down

• vertical shift down

Multiple Choice

If the blue graph is

f(x) = x²

then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Multiple Choice

Describe the transformation of

f(x) = x² -8 when compared to the parent function

• Vertical shift sp 8 units

• Vertical shift down 8 units

• Horizontal shift right 8 units

• Horizontal shift left 8 units

Multiple Choice

Describe the transformations of f(x) when compared to the parent function.

f(x)=(x+7)²

• horizontal shift left 7 units

• horizontal shift right 7 units

• vertical shift up 7 units

• vertical shift down 7 units

Multiple Choice

Which transformation maps the graph of

f(x) = x² to the graph of g(x) = (x + 4)²?

• a translation shifting f(x) 4 units up

• a translation shifting f(x) 4 units down

• a translation shifting f(x) 4 units to the left

• a translation shifting f(x) 4 units to the right

Multiple Choice

Write the equation of the quadratic function. (parabola)

• y = x² - 6

• y = x² + 6

• y = ( x - 6 )²

• y = ( x + 6 )²

Multiple Choice

Write the equation of the quadratic function. (parabola)

• y = x² - 1

• y = - x²

• y = ( - x - 1 )²

• y = ( - x + 1 )²

Multiple Choice

Match the equation to its description.

• Reflected over x, right 2 and up 1

• Reflected over x, left 2 and up 1

• Reflected over x, right 2 and down 1

• Reflected over x, left 2 and down 1

Multiple Choice

How did we transform from f(x) =x²

to

g(x) = -3x²

• reflection in x-axis and vertical shift down

• reflection x-axis and vertical stretch

• horizontal stretch

• reflection x-axis and vertical compression

Multiple Choice

How did we transform from f(x) =x²

to

g(x) = -3x²

• reflection in x-axis and vertical shift down

• reflection x-axis and vertical stretch

• horizontal stretch

• reflection x-axis and vertical compression

Multiple Choice

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down

Multiple Choice

Match the equation to its description.

• Reflected over x and stretched by 3

• Stretched by 3

• Reflected over x

• Reflected over x and up 3

Multiple Choice

Compare the function y = 5x² to the parent function y = x²

• Wider

• Narrower

Multiple Choice

What is the equation of the quadratic function obtained from vertically compressing the parent function by 3/5 and then shifted up 8 units?

• f(x)= 3/5(x-8)²

• f(x)=3/5x²+8

• f(x)=x²

• f(x)=3/5x²-8

Multiple Choice

How did we transform from the parent function?

g(x) = -1/5(x - 1)² + 7

• reflection, vertical compression, horizontal right, vertical up

• vertical compression, horizontal shift left, vertical shift up

• reflection, horizontal shift right, vertical shift down

• no changes were made to y = x²

Multiple Choice

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5
• y = 2(x + 4)² + 5
• y = -2(x - 4)² + 5
• y = -2(x + 4)² + 5

Multiple Choice

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

• Vertical Stretch by a factor of 2 and vertical shift up 4 units

• Vertical Compress by a factor 2 and vertical shift up 4

• Vertical Stretch by a factor of 2 and horizontal shift left 4 units

• Vertical Compress by a factor of 2 and horizontal shift right 4 units

Multiple Choice

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

• Vertical Stretch by a factor of 2 and vertical shift up 4 units

• Vertical Compress by a factor 2 and vertical shift up 4

• Vertical Stretch by a factor of 2 and horizontal shift left 4 units

• Vertical Compress by a factor of 2 and horizontal shift right 4 units