Find the Maximum/Minimum Value y=2x^2+28x-8

$y = 2 x^{2} + 28 x - 8$

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

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

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

$x = - \frac{28}{2 (2)}$

Remove parentheses.

$x = - \frac{28}{2 (2)}$

Simplify $- \frac{28}{2 (2)}$ .

Cancel the common factor of $28$ and $2$ .

Factor $2$ out of $28$ .

$x = - \frac{2 \cdot 14}{2 \cdot 2}$

Cancel the common factors.

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

$x = - \frac{2 \cdot 14}{2 (2)}$

Cancel the common factor.

$x = - \frac{2 \cdot 14}{2 \cdot 2}$

Rewrite the expression.

$x = - \frac{14}{2}$

Cancel the common factor of $14$ and $2$ .

Factor $2$ out of $14$ .

$x = - \frac{2 \cdot 7}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = - \frac{2 \cdot 7}{2 (1)}$

Cancel the common factor.

$x = - \frac{2 \cdot 7}{2 \cdot 1}$

Rewrite the expression.

$x = - \frac{7}{1}$

Divide $7$ by $1$ .

$x = - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$x = - 7$

Evaluate $f (- 7)$ .

Replace the variable $x$ with $- 7$ in the expression.

$f (- 7) = 2 {(- 7)}^{2} + 28 (- 7) - 8$

Simplify the result.

Simplify each term.

Raise $- 7$ to the power of $2$ .

$f (- 7) = 2 \cdot 49 + 28 (- 7) - 8$

Multiply $2$ by $49$ .

$f (- 7) = 98 + 28 (- 7) - 8$

Multiply $28$ by $- 7$ .

$f (- 7) = 98 - 196 - 8$

Simplify by subtracting numbers.

Subtract $196$ from $98$ .

$f (- 7) = - 98 - 8$

Subtract $8$ from $- 98$ .

$f (- 7) = - 106$

The final answer is $- 106$ .

$- 106$

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

$(- 7, - 106)$

Find the Maximum/Minimum Value y=2x^2+28x-8

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