# Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding: 8

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).

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