Find the Maximum/Minimum Value -3x^2-24x-46

$- 3 x^{2} - 24 x - 46$

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 $x = - \frac{b}{2 a}$ .

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

$x = - \frac{- 24}{2 (- 3)}$

Remove parentheses.

$x = - \frac{- 24}{2 (- 3)}$

Simplify $- \frac{- 24}{2 (- 3)}$ .

Cancel the common factor of $- 24$ and $2$ .

Factor $2$ out of $- 24$ .

$x = - \frac{2 \cdot - 12}{2 \cdot - 3}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 3$ .

$x = - \frac{2 \cdot - 12}{2 (- 3)}$

Cancel the common factor.

$x = - \frac{2 \cdot - 12}{2 \cdot - 3}$

Rewrite the expression.

$x = - \frac{- 12}{- 3}$

Cancel the common factor of $- 12$ and $- 3$ .

Factor $- 3$ out of $- 12$ .

$x = - \frac{- 3 (4)}{- 3}$

Cancel the common factors.

Factor $- 3$ out of $- 3$ .

$x = - \frac{- 3 \cdot 4}{- 3 \cdot 1}$

Cancel the common factor.

$x = - \frac{- 3 \cdot 4}{- 3 \cdot 1}$

Rewrite the expression.

$x = - \frac{4}{1}$

Divide $4$ by $1$ .

$x = - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$x = - 4$

Step 3

Evaluate $f (- 4)$ .

Replace the variable $x$ with $- 4$ in the expression.

$f (- 4) = - 3 {(- 4)}^{2} - 24 \cdot - 4 - 46$

Simplify the result.

Simplify each term.

Raise $- 4$ to the power of $2$ .

$f (- 4) = - 3 \cdot 16 - 24 \cdot - 4 - 46$

Multiply $- 3$ by $16$ .

$f (- 4) = - 48 - 24 \cdot - 4 - 46$

Multiply $- 24$ by $- 4$ .

$f (- 4) = - 48 + 96 - 46$

Simplify by adding and subtracting.

Add $- 48$ and $96$ .

$f (- 4) = 48 - 46$

Subtract $46$ from $48$ .

$f (- 4) = 2$

The final answer is $2$ .

$2$

Step 4

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

$(- 4, 2)$

Step 5

Find the Maximum/Minimum Value -3x^2-24x-46

Related Questions

Support LCMGCF.com by disabling your adblocker.