Question

write an equation for the function whose graph is shown to the right. the graph shows a transformation of a common function.
an equation for the function of the given graph is .
(type an equation using x and y as the variables. use integers or decimals for any numbers in the equation.)
-10,10,1 by -1,7,1

Explanation:

Step1: Identify parent function

The graph is a U-shape, so parent function is $y=x^2$.

Step2: Find horizontal shift

Vertex is at $x=2$ (shift right 2), so replace $x$ with $x-2$: $y=(x-2)^2$.

Step3: Find vertical shift

Vertex is at $y=1$ (shift up 1), so add 1: $y=(x-2)^2 + 1$.

Step4: Verify with graph range

The domain $[-10,10]$ and range $[-1,7]$ match this transformed quadratic function.

Answer:

$y=(x-2)^2 + 1$