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

A.

q − \(\frac{8}{7}\)

B.

7 − \(\frac{q}{4}\)

C.

8 − \(\frac{q}{2}\)

D.

7 + \(\frac{q}{8}\)

Correct answer is B

Y = Px2 + q

Y = 2x2 - 1

Px2 + q = 2x2 - 1

Px2 = 2x2 - 1 - q

p = \(\frac{2x^2 - 1 - q}{x^2}\)

at x = 2

P = \(\frac{2(2)^2 - 1 - q}{2^2}\)

= \(\frac{2(4) - 1 -q}{4}\)

= \(\frac{8 - 1 - q}{4}\)

P = \(\frac{7 - q}{4}\)