# Thread: graph

1. ## graph

hey sorry for the sloppy graph i attached. I don't know how to really use the graph software. And um, please don't look at the numbers on the x-axis and y-axis. I don't know how to erase them. There's number on the graph given.

The figure shows the graph of y=x^2 and y=a-x^2 for constant a. If line segment PQ=6. What does the constant "a" equal? I don't get why the answer is 18.

The attachment might seem a little small, the graph of the with concave down (opening down?) is the equation y=a-x^2 and the graph with concave graph is y=x^2. The line segment between the two graphs (between the two points they intersect) is PQ which equals 16.

2. Originally Posted by fabxx
The figure shows the graph of y=x^2 and y=a-x^2 for constant a. If line segment PQ=6. What does the constant "a" equal? I don't get why the answer is 18.
Both are quadratic functions (type of parabolas) with symmetry axis being the y-axis. So, the point where the curves of both intersect is at $x_1=-3$ and $x_2=3$. Now you only need to and equal both equations to get the point of intersection. Insert $x$ into $x^2=-x^2-a \Rightarrow 2x^2=a \Rightarrow a=18$

3. Both are quadratic functions (type of parabolas) with symmetry axis being the y-axis. So, the point where the curves of both intersect is at and . Now you only need to and equal both equations to get the point of intersection. Insert into
How do you tell they have symmetry axis being the y-axis? Thanks