Transformations of Quadratic Functions

Transformations of Quadratic Functions

Parent Function:

Multiple Choice

Name the parent function.

• quadratic

• cubic

• square root

• logarithmic

Multiple Choice

What do we call the graph of a quadratic function?

• a parabola

• a linear relationship

• a vertex

• an axis of symmetry

Multiple Choice

Which is the DOMAIN of the parent graph of a quadratic function?

• y > 0

• y = 0

• All Real Numbers

• y < 0

Multiple Choice

What is the RANGE of the parent function $$y=x^2$$ ?

• All Real Numbers

• y > 0

• x < 0

• N/A

Multiple Choice

What is the axis of symmetry for the graph of the quadratic parent function?

• y = 0 (x-axis)

• x = 0 (y-axis)

• x=1

• y=1

Vertical Shifts

​Vertical shifts translate the parabola up and down the coordinate place

Multiple Choice

Consider the parabola graphed here: $$y=\left(x-h\right)^2+k$$

• k > 0

• k = 0

• k < 0

Multiple Choice

The quadratic parent function f(x) = x² is translated up 3 units. Determine the resulting function g(x) in vertex form.

• $$g\left(x\right)=x^2-3$$

• $$g\left(x\right)=x^2+3$$

• $$g\left(x\right)=3x^2$$

• $$g\left(x\right)=\left(x+3\right)^2$$

Multiple Choice

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

Multiple Choice

Describe the transformation:

$$f\left(x\right)=x^2-5$$  

• right 5

• up 5

• left 5

• down 5

Multiple Choice

What is the range of the function $$y=-\left(x-3\right)^2-5$$

• y < -5

• y > -5

• x > -3

• y > -3

Horizontal Shifts

Horizontal shifts move the graph left and right

Multiple Choice

Determine which quadratic equation matches the table of values seen here?

• $$f\left(x\right)=-x^2+2$$

• $$f\left(x\right)=-\left(x-2\right)^2$$

• $$f\left(x\right)=\left(x+2\right)^2$$

• $$f\left(x\right)=\left(x-2\right)^2$$

Multiple Choice

Given f(x) = (x + 3)² , how did we transform from the parent function?

• Horizontal shift left 3

• Vertical shift up 3

• Horizontal shift right 3

• Vertical shift down 3

Multiple Choice

If the blue is f(x) = x^2, the red must be

• g(x) = (x + 3)²

• g(x) = (x - 3)²

• g(x) = x² + 3

• g(x) = x² - 2

Multiple Choice

What is the axis of symmetry for the following function?

f(x) = 5(x - 3)² + 7

• x = 5

• x = 7

• x = 3

• x = -3

Multiple Choice

Which of the following is the graph of $$f\left(x\right)=\left(x-1\right)^2-2$$ ?

Multiple Choice

Determine the vertex of the following quadratic function

$$f\left(x\right)=3\left(x-5\right)^2+7$$

• (7, -3)

• (3, 5)

• (5, 7)

• (2, 3)

​a is negative = opens down

a is positive = opens up

a > 1 = vertical stretch (skinny)

0 < a < 1 = vertical shrink (wider)

​Reflections,

Stretches, &

Shrinks...OH MY!

Multiple Choice

Does the quadratic have a max/min vertex, and does the parabola open up/down?

• max/ opens down

• min/ opens up

• max/ opens up

• min/ opens down

Multiple Choice

What is the vertex of the function $$y=-\left(x+5\right)^2$$ ? Does it open up or down?

• minimum at (-5, 0)

• minimum at (5, 0)

• maximum at (-5, 0)

• minimum at (-5, 0)

Multiple Choice

Does the equation open up or down?  $$y=-\left(x-5\right)^2+1$$

• up

• down

• Neither; it opens to the right.

• Neither; it opens to the left.

Multiple Choice

What is the maximum/minimum of a parabola called?

• vertex

• point

• top

• bottom

Multiple Choice

Determine the maximum or minimum of the graph of $$f\left(x\right)=-3\left(x+4\right)^2+2$$

• minimum at 4

• maximum at -4

• minimum at 2

• maximum at 2

Multiple Choice

Which of the following quadratic equations (in vertex form) have transformed from the parent function $$f\left(x\right)=x^2$$ by vertical shrink?

• $$f\left(x\right)=-2x^2$$

• $$f\left(x\right)=\frac{1}{2}x^2$$

• $$f\left(x\right)=x^2-6$$

• $$f\left(x\right)=\frac{5}{2}x^2$$

Multiple Choice

Let the graph of g be a translation 7 units right and a reflection of the graph of f(x) = x². Write a rule for g.

• g(x) = -(x - 7)²

• g(x) = (x - 7)²

• g(x) = -(x + 7)²

• g(x) = (x + 7)²

Multiple Choice

Identify the function graphed here.

• $$f\left(x\right)=\left(x+4\right)^2-2$$  

• $$f\left(x\right)=-\left(x-4\right)^2+2$$  

• $$f\left(x\right)=-\left(x+4\right)^2-2$$  

• $$f\left(x\right)=-\left(x-4\right)^2-2$$  

Multiple Choice

Identify the function graphed here.

• $$f\left(x\right)=\left(x-3\right)^2$$  

• $$f\left(x\right)=-\left(x-3\right)^2$$  

• $$f\left(x\right)=x^2+3$$  

• $$f\left(x\right)=\left(x+3\right)^2$$  

Multiple Choice

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

• Vertical stretch by a factor of 5

• Vertical shrink/compress by a factor of 5

• Reflect over x-axis

• Vertical shift up 5 units

Multiple Select

What are the transformations of $$f\left(x\right)=-\left(x+5\right)^2-2$$ in comparison to the parent function $$f\left(x\right)=x^2$$ . (SELECT ALL THAT APPLY)

• Translated right 2 units

• Reflection across the x-axis

• Translated left 5 units

• Translated up 5 units

• Translated down 2 units

Multiple Choice

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

• reflection in x-axis and vertical shift down

• reflection x-axis and vertical stretch

• horizontal stretch

• reflection x-axis and vertical compression

Multiple Choice

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

• reflection, vertical compression, horizontal right, vertical up

• vertical compression, horizontal shift left, vertical shift up

• reflection, horizontal shift right, vertical shift down

• no changes were made to y = x²

Multiple Choice

If the blue parabola represents the parent function $$f\left(x\right)=x^2$$ , which of the following vertex form equations could represent the red parabola?

• $$y=4x^2$$

• $$y=\frac{1}{4}x^2$$

• $$y=\left(x-4\right)^2$$

• $$y=-4x^2$$

Multiple Choice

Match the equation to its description.

• Reflected over x, right 2 and up 1

• Reflected over x, left 2 and up 1

• Reflected over x, right 2 and down 1

• Reflected over x, left 2 and down 1

Multiple Choice

If red represents y = x², which equation represents black?

• y = 7x²

• y = -7x²

• y = -(1/7)x²

• y = -5x²