Quadratic Transformations

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

If the blue is f(x)=x^2, then the red must be

• g(x)=x²-5

• g(x)=x²+5

• g(x)=(x-5)²

• g(x)=(x+5)²

Given f(x) = -x² , how did we transform from the parent function?

• Horizontal shift left

• Reflection over the x-axis

• Vertical shift down

• Vertical compression

What is the axis of symmetry in the function f(x) = (x-1)² +2

• x = 1

• x = -1

• x = 2

• x = -2

"a" causes the parabola to vertically ​ (a)   when a > 1.

• stretch

• compress

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

"a" causes the parabola to vertically ​ (a)   when a < 1.

• compress

• stretch

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

• Compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

• Stretched by 1/2, shifted 4 units right and 1 unit down

Label how each number transforms the function

b

c

d

e

Reflected over the x-axis

Left 3

Stretched by a factor of 2

Right 3

Moves up 7

• vertical stretch by 2, right 3, down 5.

• vertical reflection, left 3, down 5.

• vertical stretch by 2, left 3, down 5