Question

The choices are:

A)Y = (x+3) (x-5)
B)Y = (x-3) (x+5)
C)Y = x(x-2) - 15
D)Y = (x-1)^2 - 16

The correct answer is D, I just don’t understand why.

Answer 1

Let's take a look at D:

D) y = (x-1)^2 - 16 Compare this to
y = (x-h)^2 + k This is the std. equation of a parabola in vertex form.

You can see, by comparison, that h=1 and k= -16; these are the coordinates of the vertex, clearly shown in the diagram.

Since the coefficient of (x-h)^2 is +1, the graph opens upward (which the given graph confirms), and is neither compressed nor stretched vertically.