Question

Write the equation of the function of a parabola with vertex at (-1,-2) and a point

(1,-6) that lies on the curve.

Answer 1

y = -(x +1)^2 -2

Explanation:

The equation of the parabola with vertex (h, k) and vertical scale factor "a" can be written ...

y = a(x -h)^2 +k

We are given (h, k) = (-1, -2) and (x, y) = (1, -6). Putting those values into the equation, we can solve for "a".

-6 = a(1 -(-1))^2 -2

-4 = 4a . . . . . add 2, simplify

-1 = a . . . . . . divide by 4

The function has equation ...

y = -(x +1)^2 -2