Find the Maximum/Minimum Value c=800-10x+0.25x^2

$c = 800 - 10 x + 0.25 x^{2}$

Step 1

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

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

Step 2

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

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

$x = - \frac{- 10}{2 (0.25)}$

Remove parentheses.

$x = - \frac{- 10}{2 (0.25)}$

Simplify $- \frac{- 10}{2 (0.25)}$ .

Cancel the common factor of $- 10$ and $2$ .

Factor $2$ out of $- 10$ .

$x = - \frac{2 \cdot - 5}{2 \cdot 0.25}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 0.25$ .

$x = - \frac{2 \cdot - 5}{2 (0.25)}$

Cancel the common factor.

$x = - \frac{2 \cdot - 5}{2 \cdot 0.25}$

Rewrite the expression.

$x = - \frac{- 5}{0.25}$

Simplify the expression.

Divide $- 5$ by $0.25$ .

$x = - - 20$

Multiply $- 1$ by $- 20$ .

$x = 20$

Step 3

Evaluate $f (20)$ .

Replace the variable $x$ with $20$ in the expression.

$f (20) = 800 - 10 \cdot 20 + 0.25 {(20)}^{2}$

Simplify the result.

Simplify each term.

Multiply $- 10$ by $20$ .

$f (20) = 800 - 200 + 0.25 {(20)}^{2}$

Raise $20$ to the power of $2$ .

$f (20) = 800 - 200 + 0.25 \cdot 400$

Multiply $0.25$ by $400$ .

$f (20) = 800 - 200 + 100$

Simplify by adding and subtracting.

Subtract $200$ from $800$ .

$f (20) = 600 + 100$

Add $600$ and $100$ .

$f (20) = 700$

The final answer is $700$ .

$700$

Step 4

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

$(20, 700)$

Step 5

Find the Maximum/Minimum Value c=800-10x+0.25x^2

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