Write the equation of the function of a parabola with vertex at (-1,-2) and a point (1,-6) that lies on the curve.

  y = -(x +1)^2 -2

Step-by-step 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

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.