Find the equation of a parabola that has a vertex of (3,2) and contains the point (4,7)

The equation of the parabola is:

.

The equation of a parabola with vertex (h,k) is given by:

In this problem, vertex (3,2), thus , and:

It contains point (4,7), which means that when , and this is used to find a.

Thus, the equation is:

.

A similar problem is given at link

y = 5(x - 3)² + 2

Step-by-step explanation:

y = a(x - h)² + k

y = a(x - 3)² + 2

7 = a(4 - 3)² + 2

a = 5

y = 5(x - 3)² + 2