Transformations of quadratic functions

6.7-- Transformations of quadratic functions

​A1.FBF.3 Describe the effect of the transformations kf(x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f(x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph. (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.)

Parent Function of a Quadratic

• Vertex is at (0,0)

• Graph opens up

Transformations

• a - changes how wide (compressed) or narrow (stretched) the function is, direction of the opening

• h - moves the function left/right (always opposite)

• k - moves the function up and down

List the transformations

Multiple Select

Given the parent function

$$f\left(x\right)=x^2$$  , select all the transformations to the function  $$g\left(x\right)=\left(x-6\right)^2$$  

• Reflection

• Right 6

• Left 6

• Up 2

• Down 2

Multiple Choice

Which describes how the graph of $$g\left(x\right)=\left(x-1\right)^2$$ is related to the function $$f\left(x\right)=x^2$$

• translation of $$f\left(x\right)=x^2$$ up 1 unit.

• translation of $$f\left(x\right)=x^2$$ down 1 unit.

• translation of $$f\left(x\right)=x^2$$ left 1 unit.

• translation of $$f\left(x\right)=x^2$$ right 1 units.

Multiple Select

Given the parent function

$$f\left(x\right)=x^2$$  , select all the transformations to the function  $$g\left(x\right)=-\left(x-1\right)^2-2$$  

• Reflection

• Right 1

• Left 1

• Up 2

• Down 2

Drag and Drop

Which describes how the graph of $$g\left(x\right)=-6x^2$$ is related to the function $$f\left(x\right)=x^2$$ .



Dilation of $$f\left(x\right)=x^2$$ ​

Placeholder

vertically and ​

Placeholder

across the ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

stretched

reflected

x-axis

compressed

translated

y-axis

Drag and Drop

Which describes how the graph of $$g\left(x\right)=-\frac{1}{5}x^2\ +5$$ is related to the function $$f\left(x\right)=x^2$$ .



Dilation of $$f\left(x\right)=x^2$$ ​

Placeholder

vertically,​

Placeholder

across the ​

Placeholder

, and translated ​

Placeholder

5 units.

Drag these tiles and drop them in the correct blank above

compressed

reflected

x-axis

up

translated

y-axis

stretched

down

left

right

Multiple Choice

The vertex of the quadratic function f(x) = -2x² + 4x + 3 if (1, 5). If g(x) = f(x - 2), what is the vertex of g(x)

• (1, 3)

• (1, 7)

• (-1, 5)

• (3, 5)

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

In the equation f(x)=5(x+3)²-10 what does the 5 do?

• Vertical stretch by 5

• Horizontal compress by 5

• Reflect

• Move up 5

Multiple Choice

Compare the function y = 0.3x² to the parent function y = x²

• Wider

• Narrower

Multiple Choice

Compare the function y = 5x² to the parent function y = x²

• Wider

• Narrower

Multiple Select

Given the parent function

$$f\left(x\right)=x^2$$  , select all the transformations to the function  $$g\left(x\right)=\left(x+5\right)^2+1$$  

• Reflection

• Right 5

• Left 5

• Up 1

• Down 1

Multiple Select

Given the parent function

$$f\left(x\right)=x^2$$  , select all the transformations to the function  $$g\left(x\right)=-x^2+3$$  

• Reflection

• Right 3

• Left 3

• Up 3

• Down 3