If the function $$f(x) = x^2$$ is transformed to $$f(x) = \frac{1}{2}x^2$$ , what transformation has occurred?

Vertical compression by a factor of $$\frac{1}{2}$$

The function $$f(x) = -3x^2$$ is a transformation of $$f(x) = x^2$$ . What transformations have been applied?

Vertical stretch by a factor of 3 and reflection in the x-axis

Vertical compression by a factor of 3 and reflection in the x-axis

Vertical stretch by a factor of 3

Vertical compression by a factor of 3

Which transformation is represented by the function $$f(x) = (x - 2)^2 + 4$$ ?

Horizontal shift 2 units to the right and vertical shift 4 units up

Horizontal shift 2 units to the left and vertical shift 4 units up

Horizontal shift 2 units to the left and vertical shift 4 units down

Horizontal shift 2 units to the right and vertical shift 4 units down

What is the effect on the graph of $$f(x) = x^2$$ when it is transformed to $$f(x) = x^2 - 7$$ ?

Horizontal shift 7 units to the left

Horizontal shift 7 units to the right

The function $$f(x) = \frac{1}{3}x^2$$ represents which transformation of $$f(x) = x^2$$ ?

Vertical compression by a factor of $$\frac{1}{3}$$

Vertical stretch by a factor of $$\frac{1}{3}$$

Horizontal shift 3 units to the left

What transformation is applied to $$f(x) = x^2$$ to obtain $$f(x) = -\frac{1}{2}x^2$$ ?

Vertical compression by a factor of $$\frac{1}{2}$$ and reflection in the x-axis

Vertical stretch by a factor of $$\frac{1}{2}$$ and reflection in the x-axis

Vertical stretch by a factor of 2 and reflection in the x-axis

Vertical compression by a factor of 2 and reflection in the x-axis

Which transformation is represented by the function $$f(x) = (x + 3)^2 - 2$$ ?

Horizontal shift 3 units to the left and vertical shift 2 units down

Horizontal shift 3 units to the left and vertical shift 2 units up

Horizontal shift 3 units to the right and vertical shift 2 units down

Horizontal shift 3 units to the right and vertical shift 2 units up

What is the effect on the graph of $$f(x) = x^2$$ when it is transformed to $$f(x) = 4x^2$$ ?

Vertical stretch by a factor of 4

Vertical compression by a factor of 4

The function $$f(x) = -x^2 + 6$$ represents which transformations of $$f(x) = x^2$$ ?

Reflection in the x-axis and vertical shift 6 units up

Reflection in the x-axis and vertical shift 6 units down

Vertical stretch by a factor of 6

Vertical compression by a factor of 6

What transformation is applied to $$f(x) = x^2$$ to obtain $$f(x) = (x - 1)^2 + 3$$ ?

Horizontal shift 1 unit to the right and vertical shift 3 units up

Horizontal shift 1 unit to the left and vertical shift 3 units up

Horizontal shift 1 unit to the left and vertical shift 3 units down

Horizontal shift 1 unit to the right and vertical shift 3 units down

Which transformation is represented by the function $$f(x) = -2(x + 1)^2$$ ?

Reflection in the x-axis, vertical stretch by a factor of 2, and horizontal shift 1 unit to the left

Reflection in the x-axis, vertical stretch by a factor of 2, and horizontal shift 1 unit to the right

Reflection in the x-axis, vertical compression by a factor of 2, and horizontal shift 1 unit to the left

Reflection in the x-axis, vertical compression by a factor of 2, and horizontal shift 1 unit to the right

What transformation is applied to $$f(x) = x^2$$ to obtain $$f(x) = -\frac{3}{2}x^2$$ ?

Vertical stretch by a factor of $$\frac{3}{2}$$ and reflection in the x-axis

Vertical compression by a factor of $$\frac{3}{2}$$ and reflection in the x-axis

Vertical stretch by a factor of 2 and reflection in the x-axis

Vertical compression by a factor of 2 and reflection in the x-axis

Which transformation is represented by the function $$f(x) = (x - 5)^2 - 1$$ ?

Horizontal shift 5 units to the right and vertical shift 1 unit down

Horizontal shift 5 units to the left and vertical shift 1 unit up

Horizontal shift 5 units to the left and vertical shift 1 unit down

Horizontal shift 5 units to the right and vertical shift 1 unit up

The function $$f(x) = -x^2 - 9$$ represents which transformations of $$f(x) = x^2$$ ?

Reflection in the x-axis and vertical shift 9 units down

Reflection in the x-axis and vertical shift 9 units up

Vertical stretch by a factor of 9

Vertical compression by a factor of 9

What transformation is applied to $$f(x) = x^2$$ to obtain $$f(x) = (x + 2)^2 - 4$$ ?

Horizontal shift 2 units to the left and vertical shift 4 units down

Horizontal shift 2 units to the left and vertical shift 4 units up

Horizontal shift 2 units to the right and vertical shift 4 units up

Horizontal shift 2 units to the right and vertical shift 4 units down

Which transformation is represented by the function $$f(x) = -\frac{1}{3}(x - 4)^2$$ ?

Reflection in the x-axis, vertical compression by a factor of $$\frac{1}{3}$$ , and horizontal shift 4 units to the right

Reflection in the x-axis, vertical stretch by a factor of $$\frac{1}{3}$$ , and horizontal shift 4 units to the left

Reflection in the x-axis, vertical stretch by a factor of $$\frac{1}{3}$$ , and horizontal shift 4 units to the right

Reflection in the x-axis, vertical compression by a factor of $$\frac{1}{3}$$ , and horizontal shift 4 units to the left

What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?

horizontal shift left and vertical shift down

horizontal shift down and vertical shift left

horizontal shift right and vertical shift up

horizontal shift up and vertical shift right

03.14.25 Exploring Quadratic Function Transformations

Authored by TRACEY SPICHALSKY

Mathematics

9th Grade

CCSS covered

Used 18+ times

03.14.25 Exploring Quadratic Function Transformations

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MULTIPLE CHOICE QUESTION

2 mins • 3 pts

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Horizontal shift 4 units to the left

Horizontal shift 4 units to the right

Vertical shift 4 units up

Vertical shift 4 units down

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Vertical stretch

Vertical compression

Reflection in the x-axis

Horizontal shift

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Vertical stretch by a factor of 2

Vertical compression by a factor of 2

Horizontal shift 2 units to the right

Reflection in the x-axis

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Vertical stretch by a factor of 2

Horizontal shift 2 units to the left

Reflection in the x-axis

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

MULTIPLE CHOICE QUESTION

2 mins • 3 pts

Horizontal shift 6 units to the left

Horizontal shift 6 units to the right

Vertical shift 6 units up

Vertical shift 6 units down

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