If two graphs y = px2 + q and y = 2x2 -1 intersect at x = 2, find the value of p in terms q.

If two graphs y = px2 + q and y = 2x2 -1 intersect at x = 2, find the value of p in terms q.

Answer Details

To find the value of p in terms of q, we can use the given information that the two graphs intersect at x = 2. This means that at x = 2, the values of y for both graphs are the same. So, we can substitute x = 2 into both equations and set them equal to each other: px^2 + q = 2x^2 - 1 Substituting x = 2: p(2)^2 + q = 2(2)^2 - 1 4p + q = 7 Solving for p in terms of q, we can isolate p: 4p = 7 - q p = (7 - q) / 4 Therefore, the value of p in terms of q is (7 - q) / 4.