Question

The graph of a quadratic function f has a vertex (-1,-10) and passes through the point (1,2). Which of the following represents f in vertex form?

Answer 1

Answer:

(y + 10)² = 72(x + 1)

Step-by-step explanation:

If we assume the vertex of the parabola is (α,β) and the axis is parallel to the positive x-axis, then its equation is given by

(y - β)² = 4a(x - α) ........... (1)

Now, the vertex is (-1,-10).

So, the equation will become (y + 10)² = 4a(x + 1) .......... (2)

Now, (1,2) is a point on the parabola.

So, equation (2) becomes (2 + 10)² = 4a(1 + 1)

⇒ 144 = 8a

⇒ 4a = 72

Therefore, the final equation of the parabola in vertex form will be

(y + 10)² = 72(x + 1) (Answer)