Algebra Examples

$79 x - 0.2 x^{2}$

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

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

$x = - \frac{79}{2 (- 0.2)}$

Step 2.2

Remove parentheses.

$x = - \frac{79}{2 (- 0.2)}$

Step 2.3

Simplify $- \frac{79}{2 (- 0.2)}$ .

Tap for more steps...

Step 2.3.1

Multiply $2$ by $- 0.2$ .

$x = - \frac{79}{- 0.4}$

Step 2.3.2

Divide $79$ by $- 0.4$ .

$x = - - 197.5$

Step 2.3.3

Multiply $- 1$ by $- 197.5$ .

$x = 197.5$

Step 3

Evaluate $f (197.5)$ .

Tap for more steps...

Step 3.1

Replace the variable $x$ with $197.5$ in the expression.

$f (197.5) = 79 (197.5) - 0.2 {(197.5)}^{2}$

Step 3.2

Simplify the result.

Tap for more steps...

Step 3.2.1

Simplify each term.

Tap for more steps...

Step 3.2.1.1

Multiply $79$ by $197.5$ .

$f (197.5) = 15602.5 - 0.2 {(197.5)}^{2}$

Step 3.2.1.2

Raise $197.5$ to the power of $2$ .

$f (197.5) = 15602.5 - 0.2 \cdot 39006.25$

Step 3.2.1.3

Multiply $- 0.2$ by $39006.25$ .

$f (197.5) = 15602.5 - 7801.25$

Step 3.2.2

Subtract $7801.25$ from $15602.5$ .

$f (197.5) = 7801.25$

Step 3.2.3

The final answer is $7801.25$ .

$7801.25$

Step 4

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

$(197.5, 7801.25)$

Step 5