Write an equation of the parabola y = a(x – h)2 + k that satisfies the conditions.

Question

Vertex: (-3, 1); Point on the graph: (0, -8)?

Answer 1

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

Where (h, k) is vertex.

The parabola passes through (0, - 8).

Substitute (x, y) = (0, - 8) and (h, k) = (-3, 1) in y = a(x - h)² + k.

- 8 = a[(0 - (- 3)]² + 1

Solve for a.

- 8 = 9a + 1

9a = - 8 - 1

9a = - 9

a = - 1

Substitute a = -1 and (h, k) = (-3, 1) in y = a(x - h)² + k.

Required equation y = - 1(x - ( - 3)]² + 1.