Quadratic Transformations

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

• a reflection across the line x = -4
• a reflection across the line y = -4
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

What is the vertex form of a quadratic function?

• f(x) = 2a(x - h)² + k

• f(x) = a(x - h)² + k

• f(x) = (x + h)² + k

• f(x) = a(x - h) - k

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

• vertical shrink

• vertical stretch

Given f(x) = ax² , if a > 1 , the graph will transform by

• vertical shrink

• vertical stretch

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

• Horizontal shift left 6, vertical shift up 2

• Horizontal shift left 6, vertical shift down 2

• Horizontal shift right 6, vertical shift down 2

• Horizontal shift right 6, vertical shift up 2

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

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

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 equation would shift the quadratic function

 $f\left(x\right)=x^2$  up 3 units and to the right 4 units.

•  $f\left(x\right)=\left(x+3\right)^2+4$  

•  $f\left(x\right)=3\left(x-4\right)^2$  

•  $f\left(x\right)=\left(x-4\right)^2+3$  

•  $f\left(x\right)=\left(x+4\right)^2+3$  

Which equation would vertically stretch the quadratic function

 $f\left(x\right)=x^2$  by a factor of 3 and shift it 4 to the right?

•  $f\left(x\right)=\left(x+3\right)^2+4$  

•  $f\left(x\right)=3\left(x-4\right)^2$  

•  $f\left(x\right)=\left(x-4\right)^2+3$  

•  $f\left(x\right)=\left(x+4\right)2+3$  

Describe the transformation:

 $f\left(x\right)=\left(x+3\right)^2-2$  

• right 3, down 2

• up 3, left 2

• left 3, up 2

• left 3, down 2