Question

The vertex of a parabola is at (2,5) and the parabola passes through (4,-1) What is the equation of the parabola?

y=-1.5(x-5)^2+2
y=-2.5(x-2)^2+5
y=-2.5(x+2)^2+5
y=-1.5(x-2)^2+5

Answer 1

y = -1.5 (x - 2)² + 5

Explanation:

recall the formula for a parabola:

y = a(x – h)² + k

where (h, k) is the vertex

given the vertex (2,5), we have

y = a (x - 2)² + 5

We are also given that the point (4, -1) lies on our parabola

-1 = a (4 - 2)² + 5 take 5 from both sides

-6 = 4a divide both sides by 4

-1.5 = a

giving us the equation

y = -1.5 (x - 2)² + 5