<p>I don't get this Q at all. I keep getting 9 as an answer. In y=a-x^2 y is at 0 at x=3 so i plug in 3 and solve for a
0=a-(3^2)
a=9</p>
<p>but it says the answer is 18......how??</p>
<p>also what role does the y=x^2 graph play in the problem? is it just to tell that it is symmetrical and that the segment can be broken in half?</p>
<p>The graph shows two parabolas that intersect at two points. You can figure out the points they intersect at because line PQ = 6. The two parabolas intersect twice at the tail ends of this line. So you know they intersect when x = 3, and x = -3. Graph y = x^2 in your calculator and you see that when x = 3, y = 9. This is one of the points of intersection. Now all you have to do is find a graph where, when x = 3, y = 9 b/c that means that graph will intersect y = x^2 at that point. They give you values of a in the answer keys, substitute those for a and you'll see that y = 18 - x^2 intersects y = x^2 at 3,9 and -3,9.
Although this isn't a "mathy" solution you can do it quickly on your calculator. </p>
<p>As for your way of doing it, you said that y = 0 when x = 3. But that's not true. Look at the graph. When x = 3, y is definitely not 0. Its actually the point at which the two graphs intersect.</p>