Question

2

Find the equation of a parabola with a vertex at (2, 4) and a known point at (-5, 2).
f (x) =

Answer 1

f(x) = -²/₄₉(x - 2)² + 4

Explanation:

The vertex form of an equation of the parabola:

f(x) = a(x - p)² + q

vertex is (2, 4) so p = 2, q = 4

so:

f(x) = a(x - 2)² + 4

the parabola goes through the point (-5, 2) so x=-5, f(x)=2

2 = a(-5-2)² + 4

- 2 = a(49)

a = -²/₄₉

Therefore the equation of the parabola in vertex form:

f(x) = -²/₄₉(x - 2)² + 4