8.4 Homework Day 4 Graphing & Transforming Quadratic Functions (Vertex Form)

2

a) According to the EOC reference sheet, what is the vertex form of a quadratic function? _______ 
b) What transformation is missing from this format?
_______ 

1

Do horizontal transformations affect the x-values or the y-values?

1

Do vertical transformations affect the x-values or the y-values?

5

The quadratic function {𝒇(𝒙)=𝒙^𝟐−𝟑} undergoes two different dilations, creating {𝒈(x)}and {𝒉(𝒙)}, as shown below.
Complete the tables on paper. Upload your work below. (no work = no credit)
{\bold a)} Name the transformation for {g(x)}. 
_______ by a factor of _______ 

{\bold b)} Name the transformation for {h(x)}.
_______ by a factor of _______ 

{\bold c)} Which has a more extreme effect on quadratic functions: vertical or horizontal dilations? 
_______ 

10

Given a function {𝑓(𝑥)}, decide what transformation is shown in each of the following, and what the result on the graph would be by circling the given options.

	Vertical	Horizontal	Stretch	Compress	Reflection	Steeper	Flatter
𝑔(𝑥)=𝑓(−8𝑥)
𝑔(𝑥)=2𝑓(𝑥)
𝑔(𝑥)=𝑓(2𝑥)
𝑔(𝑥)=𝑓(−𝑥)
𝑔(𝑥)=\frac{1}{2}𝑓(𝑥)
𝑔(𝑥)=𝑓(\frac12𝑥)
𝑔(𝑥)=−2𝑓(𝑥)

6

Suppose that the graph of the function 𝑓(𝑥) (shown with a dashed line) is dilated in different ways.
Match each graph to its dilation.
_______ {-f(x)}

_______ {4f(x)}

_______ {f(-x)}

_______ {f(\frac 13x)}

_______ {-\frac 14f(x)}

_______ {f(4x)}

1

Several points on the graph of a quadratic function {𝒇(𝒙)} are shown in the table.

Identify the table for the transformed function defined by {𝒉(𝒙)= −\frac𝟏𝟐𝒇(𝒙)}.

Do horizontal transformations affect the x-values or the y-values?

8.4 Homework Day 4 Graphing & Transforming Quadratic Functions (Vertex Form)

Do horizontal transformations affect the x-values or the y-values?

Do vertical transformations affect the x-values or the y-values?

Given a function {𝑓(𝑥)}, decide what transformation is shown in each of the following, and what the result on the graph would be by circling the given options.

Several points on the graph of a quadratic function {𝒇(𝒙)} are shown in the table.Identify the table for the transformed function defined by {𝒉(𝒙)= −\frac𝟏𝟐𝒇(𝒙)}.

Do vertical transformations affect the x-values or the y-values?

Given a function {𝑓(𝑥)}, decide what transformation is shown in each of the following, and what the result on the graph would be by circling the given options.

Several points on the graph of a quadratic function {𝒇(𝒙)} are shown in the table.Identify the table for the transformed function defined by {𝒉(𝒙)= −\frac𝟏𝟐𝒇(𝒙)}.

Several points on the graph of a quadratic function {𝒇(𝒙)} are shown in the table.

Identify the table for the transformed function defined by {𝒉(𝒙)= −\frac𝟏𝟐𝒇(𝒙)}.

Several points on the graph of a quadratic function {𝒇(𝒙)} are shown in the table.

Identify the table for the transformed function defined by {𝒉(𝒙)= −\frac𝟏𝟐𝒇(𝒙)}.