Given that the two graphs \(y = px^2 + q\) and \(y = 2x^2 - 1\) intersect at \(x = 2\), we can find the value of \(p\) in terms of \(q\) as follows:

Since the two graphs intersect at \(x = 2\), their \(y\)-values must be equal at this point. So, we can set the two expressions for \(y\) equal to each other and substitute \(x = 2\) to get:

\(px^2 + q = 2x^2 - 1\)

\(p(2)^2 + q = 2(2)^2 - 1\)

\(4p + q = 8 - 1\)

\(4p + q = 7\)

Solving for p in terms of q, we get:

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

So, the value of p in terms of q is \(\frac{7 - q}{4}\).