What is the equation in standard form of a parabola with a focus of (-3,2) and a directrix of y=4.

Graphing y = 4 and the focus, we clearly see that the equation we need has the form (x - h)^2 = 4a(y - k).

We need to find a, h and k.

The focus is half way between the vertex and directrix.

You know that y = 4 is 2 units away from the focus and the focus is 2 units down from the focus. So, our vertex is (-3, 0).

From the vertex to the directrix, there are 4 units. Half that distance is the value of a. So, a = 2.

We have all that is needed to form our equation.

(x - (-3))^2 = 4(2)(y - 0)

(x + 3)^2 = 8y

Done.

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!

1,8,15,22,29,36,43,50

step-by-step explanation: