Writing equations of transformations

Writing equations of transformations

Please grab paper and pencil for notes

Key features of a parabola (review)

• Write down on your paper

• What are the coordinates of both x-intercepts

• What are the coordinates of the vertex

Multiple Choice

The coordinate of the vertex are

• (1,0)

• (5,0)

• (3,4)

• (0,-4)

Multiple Choice

The equation for the axis of symmetry is

• x=4

• y=3

• x=3

• y=4

This is the graph of the parent function

 $f\left(x\right)=x^2$  

• What are the coordinates of the vertex?

• What is the ARoC on the interval [0,1]?

To write the transformation equation of the parent function

 $f\left(x\right)=x^2$  

• We use (h, k) from the vertex

• We use a = the ARoC for the interval from the vertex to the first lattice point on its right

To write the transformation equation of the parent function

• We use (0, 0) from the vertex

• We use a = 1

•  $f\left(x\right)=a\left(x-h\right)^2+k$  

•  $f\left(x\right)=1\left(x-0\right)^2+0$  

Another example

What are the coordinates of the vertex?

What is the ARoC on the interval?

Multiple Choice

Given that the vertex has coordinates (0,0) and the ARoC is a=2, the transformation equation for this graph is:

• 
  

  $f\left(x\right)=\left(x-2\right)^2+0$
  

• $f\left(x\right)=2\left(x-0\right)^2+0$

• $f\left(x\right)=\left(x-0\right)^2+2$

Another example

What are the coordinates of the vertex?

What is the ARoC on the interval?

Multiple Choice

Given that the vertex has coordinates (0,0) and the ARoC is a=-1, the transformation equation for this graph is:

• 
  

   $f\left(x\right)=\left(x+1\right)^2+0$ 
  

•  $f\left(x\right)=1\left(x-0\right)^2+0$ 

•  $f\left(x\right)=\left(x-0\right)^2-1$ 

•  $f\left(x\right)=-1\left(x-0\right)^2+0$  

Using (h,k) other than (0,0)

What are the coordinates of the vertex?

What is the ARoC on the interval [1,2]?

Multiple Choice

Given that the vertex has coordinates (1,1) and the ARoC is a=1, the transformation equation for this graph is:

• 
  

   $f\left(x\right)=1\left(x+1\right)^2+1$ 
  

•  $f\left(x\right)=1\left(x-1\right)^2+1$ 

•  $f\left(x\right)=\left(x-0\right)^2-1$ 

•  $f\left(x\right)=1\left(x-1\right)^2-1$  

Ramping up

What are the coordinates of the vertex?

What is the ARoC on the interval [3,4]?

Multiple Choice

Given that the vertex has coordinates (3,4) and the ARoC is a=1, the transformation equation for this graph is:

• 
  

   $f\left(x\right)=1\left(x+3\right)^2+4$ 
  

•  $f\left(x\right)=1\left(x-4\right)^2+3$ 

•  $f\left(x\right)=1\left(x-3\right)^2+4$ 

•  $f\left(x\right)=3\left(x-4\right)^2-1$  

Ramping up

What are the coordinates of the vertex?

What is the ARoC on the interval [-2,-1]?

Multiple Choice

Given that the vertex has coordinates (-2,-1) and the ARoC is a=1, the transformation equation for this graph is:

• 
  

   $f\left(x\right)=1\left(x+2\right)^2-1$ 
  

•  $f\left(x\right)=1\left(x-2\right)^2-1$ 

•  $f\left(x\right)=1\left(x-1\right)^2-2$ 

•  $f\left(x\right)=2\left(x-1\right)^2-1$  

Putting it together

Pay attention to ARoC and Vertex!

Putting it together

Your turn

Multiple Choice

The transformation equation for this graph is:

• 
  

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

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

•  $f\left(x\right)=-1\left(x-4\right)^2-2$ 

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