Question

Quadratic Functions write the equation for each of the following. start with the graph of f(x) =x²

Answer 1

Step 1

Given :

`f(x)=x^2`

Required:

`To\text{ shrink by a factor of }(1)/(2),\text{ shift 3 units right and 2 units up.}`

The question did not state clearly if we are to shrink vertically or horizontally. So we will attend to both.

Step 2

A vertical shrink by a factor of 1/2

`\begin{gathered} f(x)=x^2 \\ f(x)\text{ = }(1)/(2)x^2 \end{gathered}`

Step 3

A vertical shrink by a factor of 1/2 and a shift 3 units to the right

`f(x)=(1)/(2)(x-3)^2`

Step 4

A vertical shrink by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up

`f(x)=\text{ }(1)/(2)(x-3)^2+2`

Step 5

A horizontal shrink by a factor of 1/2

`f(x)\text{ = }2x^2`

Step 6

A horizontal shrink by a factor of 1/2 and a shift 3 units to the right

`f(x)=2(x-3)^2_{}`

Step 7

A horizontal shrink by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up

`f(x)=2(x-3)^2+2`

Hence the answer will be

If the shrink is vertical by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up ;

`f(x)=\text{ }(1)/(2)(x-3)^2+2`

If the shrink is horizontal by a factor of 1/2, a shift 3 units to the right, and a shift of 2 units up ;

`f(x)=2(x-3)^2+2`