Find the Maximum/Minimum Value y=0.5x^2+8x+5

$y = 0.5 x^{2} + 8 x + 5$

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 $b$ .

$x = - \frac{8}{2 (0.5)}$

Remove parentheses.

$x = - \frac{8}{2 (0.5)}$

Simplify $- \frac{8}{2 (0.5)}$ .

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

Factor $2$ out of $8$ .

$x = - \frac{2 \cdot 4}{2 \cdot 0.5}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 0.5$ .

$x = - \frac{2 \cdot 4}{2 (0.5)}$

Cancel the common factor.

$x = - \frac{2 \cdot 4}{2 \cdot 0.5}$

Rewrite the expression.

$x = - \frac{4}{0.5}$

Simplify the expression.

Divide $4$ by $0.5$ .

$x = - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$x = - 8$

Step 3

Evaluate $f (- 8)$ .

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

$f (- 8) = 0.5 {(- 8)}^{2} + 8 (- 8) + 5$

Simplify the result.

Simplify each term.

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

$f (- 8) = 0.5 \cdot 64 + 8 (- 8) + 5$

Multiply $0.5$ by $64$ .

$f (- 8) = 32 + 8 (- 8) + 5$

Multiply $8$ by $- 8$ .

$f (- 8) = 32 - 64 + 5$

Simplify by adding and subtracting.

Subtract $64$ from $32$ .

$f (- 8) = - 32 + 5$

Add $- 32$ and $5$ .

$f (- 8) = - 27$

The final answer is $- 27$ .

$- 27$

Step 4

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

$(- 8, - 27)$

Step 5

Find the Maximum/Minimum Value y=0.5x^2+8x+5

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