If two graphs y = px\(^2\) + q and y = 2x\(^2\) -1 intersect at x = 2, find the value of p in terms q.
A
\(\frac{q-8}{7}\)
B
\(\frac{7-q}{4}\)
C
\(\frac{8-q}{2}\)
D
\(\frac{7+q}{8}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(y = px^{2} + q ... (i)\)
\(y = 2x^{2} - 1 ... (ii)\)
At x = 2,
(i): \(y = p(2^{2}) + q = 4p + q\)
(ii): \(y = 2(2^{2}) - 1 = 7\)
\(\therefore \text{The coordinates of the point of intersection = (2, 7)}\)
(i): \(7 = 4p + q \implies p = \frac{7 - q}{4}\)
Source: Myschool Past Questions Archive (Record #1149)