Quadratic Transformation Rules

The parent function, f(x), is transformed so that it maps into g(x). Which equation would correctly represent g(x)?

(a)  

• g(x)=f(x - 3)

• g(x)=f(x + 3)

• g(x)=f(x) + 3

• g(x)=f(x) - 2

Match the equation to its description.

• Reflected over x-axis and shifted up 4

• Reflected over x-axis and shifted down 4

• Reflected over x-axis and shifted right 4

• Reflected over x-axis and shifted left 4

• up 3

• down 3

• right 1

• left 1

• across x axis

• upward

Describe the transformation on f(x) = x².

f(x) + 7

moved ​ (a)   7

• up

• down

• left

• right

Given the equation for this parabola: y = −(x − 4)2 − 3, does this parabola have a maximum or minimum value? (a)  

• Maximum

• Minimum

How did we transform from y=x²?

• reflection over y-axis and vertical stretch

• reflection over x-axis and vertical stretch

• reflection over x-axis and horizontal compression

• reflection over y-axis and horizontal compression

If the function f(x) = x² is changed so that a new function is created, 5f(x), how does the new graph compare to f(x)?

• The graph appears wider than the graph of f(x)

• The graph appears narrower than the graph of f(x)

• The graph is shifted 5 units up above f(x)

• The graph of is shifted 5 units down below f(x)

How does the function g(x) = -x² compare the the parent function f(x)?

• The new function g(x) is reflected vertically across the x-axis

• The new function g(x) is reflected horizontally across the y-axis

• The new function g(x) has all the x-values multiplied by a -1

• The new function g(x) has been shifted 1 unit down

Which of the following shows a vertical compression of the parent function?

• 5/2f(x)²

• 3/5f(x)²

• f(4x)²

• f(3/5x)²

Which of the following shows a horizontal compression of the parent function?

• 5f(x)²

• -f(x)²

• f(2/5x)²

• f(4x)²