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})
Correct Answer: Option B
Explanation
(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})