Find the Maximum/Minimum Value g(x)=-3x^2-6x-5

$g (x) = - 3 x^{2} - 6 x - 5$

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 $b$ .

$x = - \frac{- 6}{2 (- 3)}$

Remove parentheses.

$x = - \frac{- 6}{2 (- 3)}$

Simplify $- \frac{- 6}{2 (- 3)}$ .

Cancel the common factor of $- 6$ and $2$ .

Factor $2$ out of $- 6$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Rewrite the expression.

$x = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$x = - 1$

Step 3

Evaluate $f (- 1)$ .

Replace the variable $x$ with $- 1$ in the expression.

$g (- 1) = - 3 {(- 1)}^{2} - 6 \cdot - 1 - 5$

Simplify the result.

Simplify each term.

Raise $- 1$ to the power of $2$ .

$g (- 1) = - 3 \cdot 1 - 6 \cdot - 1 - 5$

Multiply $- 3$ by $1$ .

$g (- 1) = - 3 - 6 \cdot - 1 - 5$

Multiply $- 6$ by $- 1$ .

$g (- 1) = - 3 + 6 - 5$

Simplify by adding and subtracting.

Add $- 3$ and $6$ .

$g (- 1) = 3 - 5$

Subtract $5$ from $3$ .

$g (- 1) = - 2$

The final answer is $- 2$ .

$- 2$

Step 4

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

$(- 1, - 2)$

Step 5

Find the Maximum/Minimum Value g(x)=-3x^2-6x-5

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