Transformations of Quadratics in Standard Form

Compare the graph of g(x) = x² - 5 to the graph of f(x) = x². Choose all that apply.

• Vertical stretch

• Vertical shrink/compression

• Vertical translation (shift) up

• Reflection

• Vertical translation (shift) down

Compare the graph of g(x) = -(1/4)x² + 5 to the graph of f(x) = x². Choose all that apply.

• Vertical stretch

• Vertical shrink/compression

• Vertical translation (shift) up

• Reflection

• Vertical translation (shift) down

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

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

• a vertical translation 4 units up

• a vertical translation 4 units down

• a horizontal translation 4 units to the left

• a horizontal translation 4 units to the right

How did we transform from f(x) =x² to g(x) = -3x²

• reflection in x-axis and vertical shift down

• reflection in x-axis and vertical stretch

• horizontal stretch

• reflection in x-axis and vertical compression

Describe the transformations from f(x) = x² to g(x) = -0.3x² + 4

• vertical compression and shift up

• reflection over x-axis, vertical compression, and shift up

• reflection over x-axis, vertical stretch, and shift up

• vertical stretch and shift down

Which graph will be the most vertically stretched compared to the quadratic parent function?

• g(x) = -x² + 9

• g(x) = 5x² + 1

• g(x) = 0.2x² - 11

• g(x) = -3x² - 6

Which graph will have the farthest vertical shift away from the quadratic parent function?

• g(x) = -x² + 9

• g(x) = 5x² + 1

• g(x) = 0.2x² - 11

• g(x) = -3x² - 6

Using the graph of y = -1.5x² + 12x - 23 shown here, what are the values of x when y = -5?

• x = 4

• x = 2, 6

• x = 3.2, 4.8

• cannot be determined on the graph

If a quadratic equation has 2 solutions, they will be equal distance from the axis of symmetry.

• TRUE

• FALSE