Question

Select the function that represents a parabola with vertex at (2,1) and y-intercept (0,3).

Question 10 options:

A)

ƒ(x) = 1∕2(x – 2)2 + 1

B)

ƒ(x) = 1∕2(x + 2)2 + 1

C)

ƒ(x) = 2(x + 2)2 + 1

D)

ƒ(x) = 2(x – 2)2 + 1

Answer 1

y - 1 = (1/2)(x - 2)^2

Explanation:

The appropriate equation for such a parabola has the form

y - k = a(x - h)^2, where (h, k) is the vertex:

y - 1 = a(x - 2)^2. Since the y-intercept is (0, 3), we substitute 3 for y and 0 for x, obtaining:

3 - 1 = a(0 - 2)^2, or

2 = a(4). Therefore, a = 1/2, and the equation of this parabola is:

y - 1 = (1/2)(x - 2)^2