Write the equation of the quadratic function whose vertex is at (-5,8)

Question

and passes through the point (-3,-12)?

Answer 1

Quadratic equation represents a parabola.

Standard form of parabola y = ax² + bx + c

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

Where (h, k) is vertex.

Substitute for (h, k) = (- 5, 8)  and (x, y) = (- 3, - 12) in y = a(x - h)² + k

- 12 = a(- 3 + 5)² + 8

- 12 = a(2)² + 8

- 12 = 4a + 8

4a = - 12 - 8

4a = - 20

a = - 20/4

a = - 5

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

y = - 5(x + 5)² + 8

y = - 5(x² + 25 + 10x) + 8

y = - 5x² - 125 - 50x + 8

Required equation y = - 5x²  - 50x - 117.