Question

Suppose that g(x) = x2 - 5. Which statement best compares the graph of g(x)

with the graph of f(x) = x??
A. The graph of g(x) is shifted 5 units right.
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B. The graph of g(x) is shifted 5 units up.
C. The graph of g(x) is shifted 5 units down.
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D. The graph of g(x) is shifted 5 units left.

Answer 1

Explanation:

The vertex, or work, form of a parabola is

`y=(x-h)^2+k`, where h and k are the coordinates of the vertex. If the parabola has the equation

`y=(x-2)^2+5`, the vertex is sitting at (2, 5)---> (h, k). h = 2, k = 5. If we have nothing in a set of parenthesis with the x, there is no side to side movement. Our parabola does not have any parenthesis around the x, so no side to side movement. But it does have a -5. That means that the parabola has moved DOWN 5 units from its starting position of (0, 0). -k means the parabola moves down; +k means the parabola moves up.

So our parabola has shifted 5 units down, choice C.