Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

IP 3

The line \(y=2x+k\) intersects the curve \(y=x^2-4x+7\) at points \(P\) and \(Q\). Their \(x\)-coordinates differ by \(4\).

  1. Find \(k\).

  2. Find the coordinates of \(P\) and \(Q\).

  3. Between the intersections, find the greatest vertical distance between the line and the curve, and state where it occurs.

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Answer:(a) \(k=2\); (b) \((1,4),(5,12)\); (c) greatest vertical distance \(4\) units at \(x=3\).

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