Writing Quadratic Transformations

Transformations - Slides

We will look at how to describe the effects of a translation of a quadratic function.

Essential Question

How can you describe the graph of f(x) = a (x-h)²+k, compared to the graph of f(x), if h is a negative number?

Run it back....

We will make sure to describe the vertex & the effects of reflections, vertical and horizontal compressions and stretches.

Multiple Choice

f(x) = −x³

• Vertical translation down

• Vertical compression

• Reflection over the x-axis

• Horizontal translation left

• No transformation

Multiple Choice

f(x) = 2x

• Vertical stretch

• Vertical compression

• Vertical translation up

• Reflection over the x-axis

• No Transformation

Multiple Choice

What will be the vertex (h,k) of

f(x) = 4 (x-3)² + 1 ? *Remember f(x) = a(x-h)²+k

• (3,1)

• (1,3)

• (-3,1)

• (3, -1)

• None of these.

Multiple Choice

Let the graph of g be a reflection in the x-axis of the graph of f(x) = x² - 7. Write a rule for g. *Remember -f(x) = -(x²)

• g(x) = x² + 7

• g(x) = -x² + 7

• g(x) = -x² - 7

• g(x) = -7x²

Multiple Choice

Let the graph of g be a vertical stretch by a factor of 5 of the graph of f(x) = x². Write a rule for g.

• g(x) = 5x²

• g(x) = -5x²

• g(x) = x² + 5

• g(x) = (x + 5)²

Multiple Choice

What is the vertex of this parabola?

• (1, 2)
• (-1, -2)
• (1, -2)
• (-1, 2)

Multiple Choice

What is vertex of the quadratic function x²+4x-21?

• (4, -21)

• (-2,-25)

• (2, -21)

• (4, -25)

Translations of Quadratic Functions

We fill focus on "h" and "k" to determine the horizontal and vertical shift(s) of quadratic functions.

Translations of Quadratic Functions

*Remember vertex (h,k)

If h < 0 the graph will "slide" to the right.

If h > 0 the graph will "slide to the left.

If k > 0 the graph will "slide" up

If k < 0 the graph will "slide down.

Let's begin

Lets see if we can identify the effects of translations of the parent function

Multiple Choice

Name the parent function.

• linear

• quadratic

• cubic

• logarithmic

Multiple Choice

Which transformation maps the graph of

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

• a translation shifting f(x) 4 units up

• a translation shifting f(x) 4 units down

• a translation shifting f(x) 4 units to the left

• a translation shifting f(x) 4 units to the right

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

Match the description to its equation.

Moves up 2

Moves left 4

• A

• B

• C

• D

Multiple Choice

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

• Left 3 and up 5

• Right 3 and down 5

• Left 3 and down 5

• Right 3 and up 5

Multiple Choice

The vertex of the quadratic function f(x) in the picture (2, -2). If g(x) = f(x) - 4, what is the vertex of g(x)?

• (2, -6)

• (2, 2)

• (-2, -2)

• (6, -2)

Multiple Choice

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)

• (-6, 5)

• (-4, 3)

• (-4, 7)

Multiple Choice

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

• Translation left 2 units

• Narrower

• Vertical translation up by 2 units.

• Reflection across the x-axis.

Multiple Choice

What is the vertex form of a quadratic function?

• f(x) = 2a(x-h)² + k

• f(x) = a(x-h)² + k

• f(x) = (x+h)² + k

• f(x) = a(x-h) - k

Multiple Choice

Identify the vertex of f(x) = -2(x+1)² + 3

• (h,k)

• (3, 1)

• (-1,-3)

• (-1,3)

Multiple Choice

Match the equation to its description.

• Reflected over x and up 4
• Reflected over x and down 4
• Reflected over x and right 4 
• Reflected over x and left 4

Open Ended

How can you describe the graph of f(x) = a (x-h)²+k, compared to the graph of f(x), if h is a negative number?