Question 20187
Hello There:

First of all, you should recognize the expression on the right side of the equals sign to be a quadratic expression.  In other words, it's in the form of:

y = a*x^2 + b*x + c

Hopefully you know that the graph is going to be a parabola.

We have:

y = -x^2 + 16

Right away, we see that the parabola opens downward because the value of "a" is negative.

There are formulas for the x- and y-coordinates of the vertex point.

x-coordinate = -b/(2*a)

y-coordinate = c - b^2/(4*a)

Our equation shows that:

a = -1

b = 0

c = 16

Substitute these values into the formula above to find that (0, 16) is the vertex point.

The expression 16 - x^2 can be factored as a difference of squares.

(4 + x)*(4 - x)=0

So, the x-intercepts of the graph are (-4, 0) and (4, 0).

Pick some other values of x, and find the corresponding values of y to get a few more points to plot.  Then draw the parabola using a smooth curve that goes through all of the points that you have plotted.

~ Mark