Find the Maximum/Minimum Value r(p)=-2.5p^2+850p

$r (p) = - 2.5 p^{2} + 850 p$

The maximum of a quadratic function occurs at $x = - \frac{b}{2 a}$ . If $a$ is negative, the maximum value of the function is $f (- \frac{b}{2 a})$ .

$f_{max}$ $p = a p^{2} + b p + c$ occurs at $p = - \frac{b}{2 a}$

Find the value of $p = - \frac{b}{2 a}$ .

Substitute in the values of $a$ and $b$ .

$p = - \frac{850}{2 (- 2.5)}$

Remove parentheses.

$p = - \frac{850}{2 (- 2.5)}$

Simplify $- \frac{850}{2 (- 2.5)}$ .

Cancel the common factor of $850$ and $2$ .

Factor $2$ out of $850$ .

$p = - \frac{2 \cdot 425}{2 \cdot - 2.5}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 2.5$ .

$p = - \frac{2 \cdot 425}{2 (- 2.5)}$

Cancel the common factor.

$p = - \frac{2 \cdot 425}{2 \cdot - 2.5}$

Rewrite the expression.

$p = - \frac{425}{- 2.5}$

Simplify the expression.

Divide $425$ by $- 2.5$ .

$p = - - 170$

Multiply $- 1$ by $- 170$ .

$p = 170$

Evaluate $f (170)$ .

Replace the variable $p$ with $170$ in the expression.

$r (170) = - 2.5 {(170)}^{2} + 850 (170)$

Simplify the result.

Simplify each term.

Raise $170$ to the power of $2$ .

$r (170) = - 2.5 \cdot 28900 + 850 (170)$

Multiply $- 2.5$ by $28900$ .

$r (170) = - 72250 + 850 (170)$

Multiply $850$ by $170$ .

$r (170) = - 72250 + 144500$

Add $- 72250$ and $144500$ .

$r (170) = 72250$

The final answer is $72250$ .

$72250$

Use the $x$ and $y$ values to find where the maximum occurs.

$(170, 72250)$

Find the Maximum/Minimum Value r(p)=-2.5p^2+850p

Related Questions

Support LCMGCF.com by disabling your adblocker.