The equation in vertex form is:

y – k = a(x – h)^2

The coefficient of x^2 is a. As the graph is to open downwards, a must be negative, so that the vertex (h, k) is at the top of the graph rather than at the bottom.

Substitute the values given for h and k.

Then use the second point to find the value of a.

If you don’t want to see the rest of the answer until you’ve tried it, don’t read any further yet.

As the vertex is to be (0, -1/2), h = 0 and k = -1/2.

That gives:

y + 1/2 = ax^2

Putting x = -4, y = -97/2:

-97/2 + 1/2 = 16a

a = -96/32

= -3.

The equation is therefore:

y + 1/2 = -3x^2

y = -3x^2 -1/2.