Find the Maximum/Minimum Value f(x)=x^2+18x+79

$f (x) = x^{2} + 18 x + 79$

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 $b$ .

$x = - \frac{18}{2 (1)}$

Remove parentheses.

$x = - \frac{18}{2 (1)}$

Simplify $- \frac{18}{2 (1)}$ .

Cancel the common factor of $18$ and $2$ .

Factor $2$ out of $18$ .

$x = - \frac{2 \cdot 9}{2 \cdot 1}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 1$ .

$x = - \frac{2 \cdot 9}{2 (1)}$

Cancel the common factor.

$x = - \frac{2 \cdot 9}{2 \cdot 1}$

Rewrite the expression.

$x = - \frac{9}{1}$

Divide $9$ by $1$ .

$x = - 1 \cdot 9$

Multiply $- 1$ by $9$ .

$x = - 9$

Step 3

Evaluate $f (- 9)$ .

Replace the variable $x$ with $- 9$ in the expression.

$f (- 9) = {(- 9)}^{2} + 18 (- 9) + 79$

Simplify the result.

Simplify each term.

Raise $- 9$ to the power of $2$ .

$f (- 9) = 81 + 18 (- 9) + 79$

Multiply $18$ by $- 9$ .

$f (- 9) = 81 - 162 + 79$

Simplify by adding and subtracting.

Subtract $162$ from $81$ .

$f (- 9) = - 81 + 79$

Add $- 81$ and $79$ .

$f (- 9) = - 2$

The final answer is $- 2$ .

$- 2$

Step 4

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

$(- 9, - 2)$

Step 5

Find the Maximum/Minimum Value f(x)=x^2+18x+79

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