Finite Math Examples

$f (x) = x^{2} - 6 x + 5$

The maximum or minimum of a quadratic function occurs at $x = - \frac{b}{2 a}$ . If $a$ is negative, the maximum value of the function is $f (- \frac{b}{2 a})$ . 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 $x$ equal to $- \frac{b}{2 a}$ .

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

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

$x = - \frac{- 6}{2 (1)}$

Remove the extra parentheses from the expression $- \frac{- 6}{2 (1)}$ .

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Remove the parentheses from the numerator.

$x = \frac{6}{2 (1)}$

Remove the parentheses from the denominator.

$x = \frac{6}{2 (1)}$

Reduce the expression by cancelling the common factors.

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Factor $2$ out of $6$ .

$x = \frac{2 \cdot 3}{2 \cdot 1}$

Cancel the common factors.

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

$x = \frac{2 \cdot 3}{2 (1)}$

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 1}$

Rewrite the expression.

$x = \frac{3}{1}$

Divide $3$ by $1$ .

$x = 3$

Replace the variable $x$ with $3$ in the expression.

$f (3) = {(3)}^{2} - 6 \cdot 3 + 5$

Simplify the result.

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Simplify each term.

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Remove parentheses.

$f (3) = 3^{2} - 6 \cdot 3 + 5$

Raise $3$ to the power of $2$ .

$f (3) = 9 - 6 \cdot 3 + 5$

Multiply $- 6$ by $3$ .

$f (3) = 9 - 18 + 5$

Simplify by adding and subtracting.

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Subtract $18$ from $9$ .

$f (3) = - 9 + 5$

Add $- 9$ and $5$ .

$f (3) = - 4$

The final answer is $- 4$ .

$- 4$

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

$(3, - 4)$

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