Transformations of Quadratic Functions

What is the vertex form of a quadratic function?

Write the equation of the quadratic function. (parabola)

• y = x² - 8

• y = x² + 8

• y = ( x - 8 )²

• y = ( x + 8 )²

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

Which transformation will occur if f(x) = x² is replaced with -f(x)?

• Nothing happens, it stays the same.
• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)
• (-6, 5)
• (-4, 3)
• (-4, 7)

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

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

What transformations have occurred? 

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2