If two graphs y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q
Question 1 Report
If two graphs y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q
Answer Details
To solve the problem, we need to use the fact that the two graphs intersect at x = 2, which means that they have the same y-coordinate at that point.
Let's first find the y-coordinate of the point of intersection by plugging x = 2 into both equations:
y = p(2)^2 + q = 4p + q
y = 2(2)^2 - 1 = 7
Since the two graphs intersect at x = 2, we know that their y-coordinates are equal at that point. Therefore, we can set the two expressions for y equal to each other:
4p + q = 7
Now we can solve for p in terms of q by isolating p on one side of the equation:
4p = 7 - q
p = (7 - q) / 4
So the value of p in terms of q is (7 - q) / 4.
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