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 -4,5,1

Explanation:

Step1: Identify parent function

The graph is a parabola, so parent function is $y=x^2$.

Step2: Find vertex shift

Vertex of the given graph is $(2, -1)$. For $y=(x-h)^2+k$, $h=2$, $k=-1$.

Step3: Verify vertical stretch

Test a point: when $x=3$, $y=0$. Substitute into $y=a(x-2)^2-1$:
$0=a(3-2)^2-1$
$0=a-1$
$a=1$

Answer:

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