i Express 2x 2 4x 1 in the form a(x b) 2 c and hence state the coordinates of the minimum point, A, on the curve y 2x 2 4x 1 The line x y 4 0 intersects the curve y 2x 2 4x 1 at the points P and Q It is given that the coordinates of P are (3, 7) ii Find the coordinates of Q iii Find the equation of...

i To express the quadratic expression 2x2 4x 1 in the form ax b2 c we need to comple ...

i. Express 2x 2 4x + 1 in the form a(x + b) 2 + c

Question:

i. Express 2x² − 4x + 1 in the form a(x + b)² + c and hence state the coordinates of the minimum point, A, on the curve y = 2x² − 4x + 1. The line x − y + 4 = 0 intersects the curve y = 2x² − 4x + 1 at the points P and Q. It is given that the coordinates of P are (3, 7).

ii. Find the coordinates of Q.

iii. Find the equation of the line joining Q to the mid-point of AP.

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