If two graphs y = px2 + q and y = 2x2 -1 intersect at x = 2, find the value of p in terms q.
Answer Details
The value of p can be found by solving for p when the two equations intersect at x=2. To do this, we first need to find the y-values for both equations when x=2.
When x=2, the first equation becomes:
y = p * 2^2 + q = 4p + q
And the second equation becomes:
y = 2 * 2^2 - 1 = 7
Now we have two equations with two unknowns (p and q) and we can use substitution to solve for p. We substitute the value of y from the second equation into the first equation:
4p + q = 7
And then we can isolate p by subtracting q from both sides:
4p = 7 - q
And finally, dividing both sides by 4:
p = (7 - q) / 4
So the answer is: p = (7 - q) / 4.