Write an equation of a parabola in vertex form. Vertex (2,-3) and passes through (0,5)

Step-by-step explanation:

The vertex form of a parabola is given by y = a (x - h) ^2 + k, where (h, k) is the vertex.

Given vertex at (2,-3), h = 2, k = - 3

y = a (x - 2) ^2 + (-3) = a (x - 2) ^2 - 3

The parabola passes through (0,5) so

5 = a (0 - 2) ^2 - 3

5 = 4a - 3

4a = 8

a = 2

The parabola equation in vertex form:

y = 2 (x - 2) ^2 - 3