Find the Maximum/Minimum Value y=x^2+16x+28

$y = x^{2} + 16 x + 28$

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 $b$ .

$x = - \frac{16}{2 (1)}$

Remove parentheses.

$x = - \frac{16}{2 (1)}$

Simplify $- \frac{16}{2 (1)}$ .

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

Factor $2$ out of $16$ .

$x = - \frac{2 \cdot 8}{2 \cdot 1}$

Cancel the common factors.

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

$x = - \frac{2 \cdot 8}{2 (1)}$

Cancel the common factor.

$x = - \frac{2 \cdot 8}{2 \cdot 1}$

Rewrite the expression.

$x = - \frac{8}{1}$

Divide $8$ by $1$ .

$x = - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$x = - 8$

Step 3

Evaluate $f (- 8)$ .

Replace the variable $x$ with $- 8$ in the expression.

$f (- 8) = {(- 8)}^{2} + 16 (- 8) + 28$

Simplify the result.

Simplify each term.

Raise $- 8$ to the power of $2$ .

$f (- 8) = 64 + 16 (- 8) + 28$

Multiply $16$ by $- 8$ .

$f (- 8) = 64 - 128 + 28$

Simplify by adding and subtracting.

Subtract $128$ from $64$ .

$f (- 8) = - 64 + 28$

Add $- 64$ and $28$ .

$f (- 8) = - 36$

The final answer is $- 36$ .

$- 36$

Step 4

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

$(- 8, - 36)$

Step 5

Find the Maximum/Minimum Value y=x^2+16x+28

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