Maximization of a Quadratic Expression

Hard Algebra Expressions, Equations, And Inequalities

Consider the expression:

$$P(x) = 3x^2 - 2x + 5$$

What value of $$x$$ maximizes the expression $$P(x)$$, and what is the maximum value at that point?

The maximum occurs at $$x = \frac{1}{3}$$ with maximum value $$P\left(\frac{1}{3}\right) = 5\frac{2}{9}$$

The maximum occurs at $$x = 1$$ with maximum value $$P(1) = 6$$

The maximum occurs at $$x = -\frac{1}{3}$$ with maximum value $$P\left(-\frac{1}{3}\right) = 4$$

The quadratic has no maximum value since the leading coefficient is positive.

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