Compare Quadratic Function to Parent Function

If the blue graph is
f(x) = x² 
then the red must be...

• g(x) = x² - 5
• g(x) = x² + 5
• g(x) = (x - 5)²
• g(x) = (x + 5)²

Describe the transformations of f(x) when compared to the parent function.

g(x)=x²+5

• horizontal shift right 5 units

• horizontal shift left 5 units

• vertical shift up 5 units

• vertical shift down 5 units

How does the graph of g(x) =(7x) ² compare to the parent function f(x) = x²

• y = 7x² is wider than y = x²

• y =7x ² is narrower than y = x²

• y = 7x ² is shifted down 7 spaces from y = x²

• y = 7x ² is shifted up 7 spaces from y = x²

What is the equation of the parent function?

• f(x)=ax²+bx+c

• f(x)=x²

• f(x)=x

• f(x)=mx+b

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

• Nothing happens, it stays the same.

• Vertical stretch by a factor of 2.

• Vertical translation up by 2 units.

• Reflection across the x-axis.

Write the equation for g(x), the parabola in blue.

f(x)= x²

• g(x)= x² + 2

• g(x)= (x + 2)²

• g(x)= (x − 2)²

• g(x)= ½x²

The graph of m(x) = x² was transformed to create the graph of n(x) = m(x) +5. Which of these describes the transformation?

• The graph of n is a reflection of the graph of m on the x-axis

• The vertex of the graph n is 5 units to the left of the vertex of the graph m

• The graph of n is a reflection of the graph of m on the x-axis

• The vertex of the graph n is 5 units above the vertex of the graph m

The graph of g(x)=x² was transformed to create the graph of h(x) =-0.5x² . WHich of these describe the transformation from the graph of g to the graph of h?

• A reflection over the x-axis and a vertical stretch

• A reflection over the y-axis and a horizontal shrink

• A reflection over the x-axis and a vertical shrink

• A reflection over the y-axis and a horizontal stretch

• Reflection over the y-axis and a vertical shrink

• Reflection over the x-axis and a vertical stretch

• Reflection over the x-axis and a horizontal shrink

• Reflection over the y-axis and a horizontal stretch 

The graph of f(x)=x² is transformed to create the graph of

h(x) = (x-8)² . Which of these describe this transformation?

• A Vertical shift up 8 units

• A Vertical shift down 8 units

• A Horizontal shift to the right 8 units

• A Horizontal shift to the left 8 units