Finite Math Examples

$f (x) = 3 x^{2} + 4$

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 $b$ .

$x = - \frac{0}{2 (3)}$

Remove the extra parentheses from the expression $- \frac{0}{2 (3)}$ .

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Remove the parentheses from the numerator.

$x = - \frac{0}{2 (3)}$

Remove the parentheses from the denominator.

$x = - \frac{0}{2 (3)}$

Simplify $- \frac{0}{2 (3)}$ .

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Cancel the common factor of $0$ and $2$ .

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Factor $2$ out of $0$ .

$x = - \frac{2 (0)}{2 (3)}$

Cancel the common factors.

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Cancel the common factor.

$x = - \frac{2 \cdot 0}{2 \cdot 3}$

Rewrite the expression.

$x = - \frac{0}{3}$

Cancel the common factor of $0$ and $3$ .

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Factor $3$ out of $0$ .

$x = - \frac{3 (0)}{3}$

Cancel the common factors.

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Factor $3$ out of $3$ .

$x = - \frac{3 \cdot 0}{3 \cdot 1}$

Cancel the common factor.

$x = - \frac{3 \cdot 0}{3 \cdot 1}$

Rewrite the expression.

$x = - \frac{0}{1}$

Divide $0$ by $1$ .

$x = - 0$

Multiply $- 1$ by $0$ .

$x = 0$

Replace the variable $x$ with $0$ in the expression.

$f (0) = 3 {(0)}^{2} + 4$

Simplify the result.

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Simplify each term.

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Raising $0$ to any positive power yields $0$ .

$f (0) = 3 \cdot 0 + 4$

Multiply $3$ by $0$ .

$f (0) = 0 + 4$

Add $0$ and $4$ .

$f (0) = 4$

The final answer is $4$ .

$4$

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

$(0, 4)$

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