Answer
Option (E)
Work Step by Step
The graph involves a parabola, so its parent function is $y=x^2$.
The vertex of the parent function is at $(0, 0)$.
The vertex of the given function is at $(2, 0)$, which involves a 2-unit horizontal shift of the parent function.
Thus, a tentative equation of the function is $y=a(x-2)^2$
To find the value of $a$, substitute the x and y value of any non-vertex point on the graph. The graph passes through the point $(3, 1)$:
$y=a(x-2)^2
\\1=a(3-2)^2
\\1 = a(1^2)
\\1=a$
The equation of the function is $y=(x-2)^2$.
Therefore, the answer is Option (E).
