Write the equation of a parabola that has vertex (2.5, 2.75) and passes throught the point (1,5).

y = (x - 2.5)^2 + 2.75

Explanation:

y = a(x - h)^2 + k - Vertex form

y = a(x - 2.5)^2 + 2.75 - Replacing h with 2.5 and k with 2.75

5 = a(1 - 2.5)^2 + 2.75 - Replacing x with 1 and y with 5

5 = 2.25a + 2.75 - Doing (1 - 2.5)^2 = 2.25 times a = 2.25a

2.25 = 2.25a - Subtracting 2.75 on both sides

a = 1

y = 1(x - 2.5)^2 + 2.75 - Replacing a with 1

So the equation of a parabola is y = (x - 2.5)^2 + 2.75