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

Question

asked Aug 6, 2023 123k views

1 Answer

Matt Joiner · Answer 1 · 2023-08-09T21:11:31+0000

Step 1

Given :

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

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

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 ;