Question

Write an equation for the parabola whose vertex is at (4, 12) and which passes through (5, 21)

Answer 1

y - 12 = 9(x - 4)

Explanation:

The vertex (h, k) is (4, 12) and the point (5, 21) is on the graph. Assuming that this is a vertical parabola, opening up (because the coordinate 21 is greater than the coordinate 12), we insert the knowns into y - k = a(x - h)^2, obtaining

21 - 12 = a(5 - 4), or 9 = a. With a known, we can write the desired equation:

y - 12 = 9(x - 4)