Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

IP 3

A downward-opening parabola has \(x\)-intercepts \(1\) and \(5\), and passes through \((0,-10)\).

  1. Find its equation.

  2. Find its maximum value.

  3. Determine how many intersections it has with \(y=k\) for each possible range of \(k\).

  4. Find the intersections when \(k=6\).

Solution:

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Answer:(a) \(y=-2x^2+12x-10\); (b) \(8\); (c) Two if \(k<8\), one if \(k=8\), none if \(k>8\); (d) \((2,6),(4,6)\)

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