Question

13.If a parabola is known to have a minimum at the point (5,3), which of the followingformulas could represent the parabola? (Show work or explain!)(A)f(x) = (x - 3)2 + 5(B)f(x) = (x - 5)2 + 3(C)f(x) = 5(x + 3)2 + 5(D)f(x) = -2(x + 3)2 + 5(E)f(x) = -5(x - 3)2 + 5

Answer 1

The vertex form of a parabola is:

y = a(x - h)² + k

where (h, k) is the vertex

The vertex is the minimum or the maximum of the curve. Then, in this case,

h = 5

k = 3

If a is positive, then the graph has a U shape, but if it's negative it has the form of an inverted U. Given that the point (5,3) is a minimum, then a is positive.

Therefore, options D and E are incorrect. From options A, B and C, the only one that could be correct is:

(B)f(x) = (x - 5)² + 3