Quadratic Function Dilations

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1

• f(x) = (x + 2)² - 1

• f(x) = -(x + 2)² - 1

• f(x) = -(x - 2)² - 1

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = 2x²

• g(x) = 1/2x²

• g(x) = x² + 2

• g(x) = (x + 2)²

Label how each number transforms the function

b

c

d

e

Reflected over the x-axis

Stretched by a factor of 2

Moves up 7

Left 3

Right 3

• Reflection over x-axis

• None of these

Match the equation to its description.

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 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

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

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

• vertical shift down

• vertical stretch

• horizontal stretch

• vertical compression

How did we transform from the parent function? g(x) = 1/5(x - 1)² + 7

• vertical compression, horizontal right, vertical up

• vertical compression, horizontal shift left, vertical shift up

• horizontal shift right, vertical shift down

• no changes were made to y = x²

What are transformations in the context of quadratic functions?

• Changes to the graph, including translations, reflections, and dilations.

• The highest point on the graph.

• The lowest point on the graph.

• The set of all possible input values.