Transforming Quadratic Equations

Which function has a translation of 2 units right and a vertical stretch by a factor of 5?

• f(x)= 5(x - 2)²

• f(x) = 5(x + 2)²

• f(x) = (x - 2)² - 5

• f(x) = (x + 2)² + 5

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

Which function has a translation of 3 units to the left?

• f(x) = 3x²+1

• f(x) = (x + 3)² + 1

• f(x) = (x - 3) ²+ 1

• f(x) = (x + 1)²- 3

Which function has a translation of 7 units down and reflects over the x-axis?

• f(x) = -(x - 7)² + 1

• f(x) = (x + 7)² + 1

• f(x) = -(x - 1)² - 7

• f(x) = (x + 1)² - 7

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

Label how each number transforms the function

b

c

d

e

Moves up 7

Reflected over the x-axis

Right 3

Left 3

Stretched by a factor of 2

a

b

c

d

e

reflected

up

right

left

down

a

b

c

d

Horizontal Dilation

Vertical Dilation

Vertical Translation

Horizontal Translation

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

• stretch

• compress

Identify the possible functions that matches each specific transformation listed from the parent function f(x) = x^2

a

b

c

d