need help

Question

determine the equation of the parabola with a vertex (-2,3) and passes through the point (0,-13) .

Answer 1

Vertex form of parabola is y = a(x - h)² + k

Vertex of parabola is (h, k) = (-2, 3)

Substitute the values in above standard form.

y = a(x - (-2))² + 3

Now the equation is y = a (x + 2)² + 3

The parabola passes through the point (0, -13)

Substitute for (x, y) = (0, -13) in above equation.

- 13 = a (0 + 2)² + 3

- 13 = 4a + 3

4a = - 13 - 3

4a = - 16

a = -16/4

a = -4

Substitute  the value of a  in y = a (x + 2)² + 3.

The equation of parabola is y = - 4 (x + 2)² + 3.