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# If two graphs y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of...

### Question

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

### Options

A) q − $$\frac{8}{7}$$

B) 7 − $$\frac{q}{4}$$

C) 8 − $$\frac{q}{2}$$

D) 7 + $$\frac{q}{8}$$

### Explanation:

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 = $$\frac{7 - q}{4}$$

## Dicussion (1)

• 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 = $$\frac{7 - q}{4}$$