Quadratic Transformations

Which function represents the transformations below?

-reflected over the x-axis

-translated 6 units left

• $y=\left(x-6\right)^2$

• $y=-\left(x-6\right)^2$

• $y=x^2-6$

• $y=-\left(x+6\right)^2$

Which function represents the transformations below?

-vertically stretched by a factor of 3

-translated 4 units up

• $y=\frac{1}{3}x^2+4$

• $y=3x^2+4$

• $y=\frac{1}{3}\left(x+4\right)^2$

• $y=3\left(x-4\right)^2$

Write an equation to represent the function that is reflected over the x-axis, then translated 8 units left and 3 units up. NO SPACES.

The graph above represents the parent function  $y=x^2$ . Which graph best illustrates the graph of the equation  $y=\frac{1}{3}x^2-3$  ?

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Gerald is testing a computer graphics program. He needs to insert a parabolic shape by transforming the quadratic parent function, f(x) = x². Gerald needs the parabolic shape to open downward, stretch vertically by a factor of 2, shift right by 3 units, and shift down by 4 units. Which transformed function should Gerald enter into the computer graphics program to achieve this result?

• g(x) = –2(x – 3)² – 4

• g(x) = 2(x – 3)² – 4

• g(x) = –2(x + 3)² – 4

• g(x) = 2(x + 3)² – 4

The graph of f(x) = x² was transformed to create the graph of g(x) = (x + 7.5)². Which of these describes this transformation?

• A horizontal shift to the right 7.5 units

• A horizontal shift to the left 7.5 units

• A vertical shift down 56.25 units

• A vertical shift up 56.25 units

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?

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