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?

(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)

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.