The graphs below have the same shape. What is the equation of the blue graph? g(x) =
A. g(x) = (x + 3)2 + 1
B. g(x) = (x - 3)2 + 1
C. g(x) = (x - 3)2 - 1
D. g(x) = (x + 3)2 - 1

Explanation:

The vertex of a parabola is either the highest point or the lowest point, depending on how the parabola is oriented. In this case, it is the lowest point.

For the red f(x) curve, we see the vertex is (0,0)

The blue g(x) curve has its vertex at (3,1)

In general, the vertex is represented by (h,k)

For the blue curve, (h,k) = (3,1) so h = 3 and k = 1 pair up together

We will plug those values along with a = 1 into the vertex form below

y = a(x-h)^2 + k

y = 1(x-3)^2 + 1

y = (x-3)^2 + 1

The blue curve is the result of shifting the red curve 3 units to the right and 1 unit up. No vertical stretching or compressing has been applied, which is why a = 1 stays the same.

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