Show, by considering its minimum, that (x) x 2 2x 3 takes on only positive values More generally, find the conditions on r and s under which the quadratic function (x) x 2 rx s takes on only positive values Give examples of r and s for which f takes on both positive and negative values ...

Observe that fx x 2x 3 x 1 2 0 for all x Let f ...

Show, by considering its minimum, that (x) = x 2 2x + 3 takes on only

Question:

Show, by considering its minimum, that ƒ(x) = x²− 2x + 3 takes on only positive values. More generally, find the conditions on r and s under which the quadratic function ƒ(x) = x² + rx + s takes on only positive values. Give examples of r and s for which f takes on both positive and negative values.

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