Find the Maximum/Minimum Value -2x^2-16x-29

$- 2 x^{2} - 16 x - 29$

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

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

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

$x = - \frac{- 16}{2 (- 2)}$

Remove parentheses.

$x = - \frac{- 16}{2 (- 2)}$

Simplify $- \frac{- 16}{2 (- 2)}$ .

Cancel the common factor of $- 16$ and $2$ .

Factor $2$ out of $- 16$ .

$x = - \frac{2 \cdot - 8}{2 \cdot - 2}$

Cancel the common factors.

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

$x = - \frac{2 \cdot - 8}{2 (- 2)}$

Cancel the common factor.

$x = - \frac{2 \cdot - 8}{2 \cdot - 2}$

Rewrite the expression.

$x = - \frac{- 8}{- 2}$

Cancel the common factor of $- 8$ and $- 2$ .

Factor $- 2$ out of $- 8$ .

$x = - \frac{- 2 (4)}{- 2}$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$x = - \frac{- 2 \cdot 4}{- 2 \cdot 1}$

Cancel the common factor.

$x = - \frac{- 2 \cdot 4}{- 2 \cdot 1}$

Rewrite the expression.

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

Divide $4$ by $1$ .

$x = - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$x = - 4$

Evaluate $f (- 4)$ .

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

$f (- 4) = - 2 {(- 4)}^{2} - 16 \cdot - 4 - 29$

Simplify the result.

Simplify each term.

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

$f (- 4) = - 2 \cdot 16 - 16 \cdot - 4 - 29$

Multiply $- 2$ by $16$ .

$f (- 4) = - 32 - 16 \cdot - 4 - 29$

Multiply $- 16$ by $- 4$ .

$f (- 4) = - 32 + 64 - 29$

Simplify by adding and subtracting.

Add $- 32$ and $64$ .

$f (- 4) = 32 - 29$

Subtract $29$ from $32$ .

$f (- 4) = 3$

The final answer is $3$ .

$3$

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

$(- 4, 3)$

Find the Maximum/Minimum Value -2x^2-16x-29

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