Transformations of the Quadratic Parent Function

Transformations of the Quadratic Parent Function

Objectives

• Graph transformations of the quadratic parent functions.

• Identify and distinguish among transformations.

• Compare functions represented in different ways.

VOCABULARY

• Parent functions are the simplest form of a given family of functions.

• The graph of a quadratic function is a curve called a parabola.

• The vertex of a parabola is the point where the parabola crosses its axis. 

• The axis of symmetry of a parabola is a line about which the parabola is symmetrical

• A reflection of a graph is the mirror image of the graph over a line.

What type of parent function is this?

Multiple Choice

Choose the correct quadratic parent function.

•  $y=\left|x\right|$  

•  $y=x^2$  

•  $y=x$  

Open Ended

Identify the vertex of

 $f\left(x\right)=-2\left(x-4\right)^2-3$  

Multiple Choice

Examine the function  $r\left(x\right)=2\left(x\ -\ 4\right)^2+3$  

a. Describe the transformations from the graph of  $f\left(x\right)\ =\ x^2$  to the graph of  $r\left(x\right)=2\left(x-4\right)^2+3$  .

• Vertical Stretch of 2, horizontal translation 4 units to the right, and a vertical translation 3 unit up.

• Vertical Stretch of 2, horizontal translation 4 units to the left, and a vertical translation 3 unit up.

• Vertical Stretch of 2, horizontal translation 4 units to the right, and a vertical translation 3 unit down

• Vertical Stretch of -2, horizontal translation 4 units to the right, and a vertical translation 3 unit up.

Open Ended

Describe the horizontal and vertical translation of

 $f\left(x\right)=3\left(x-2\right)^2-4$  

Now, let's graph a quadratic function!

 $f\left(x\right)=3\left(x-2\right)^2-4$  

• Step 1: Identify the vertex (h,k)

• Step 2: Create a table of values for x (I like to choose 2 numbers greater than and 2 numbers less than the vertex).

• Step 3: Plot your points

• Step 4: Connect your points with a smooth curve

This is what your graph should look like!

Multiple Choice

Identify the axis of symmetry.

• x = 2

• -4

• x = 3

• 2

Let's graph one more quadratic function!

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

• Step 1: Identify the vertex

• Step 2: Create a table of values

• Step 3: Plot your points

• Step 4: Plot your points with a smooth curve

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

Open Ended

EXIT TICKET
Without graphing, compare the graph 

 $f\left(x\right)=-3\left(x-4\right)^2+2$  to the quadratic parent function.