Finite Math Examples

$f (x) = 0.6 x^{2} + 3 x + 4$

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

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Step 2.1

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

$x = - \frac{3}{2 (0.6)}$

Step 2.2

Remove parentheses.

$x = - \frac{3}{2 (0.6)}$

Step 2.3

Simplify $- \frac{3}{2 (0.6)}$ .

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Step 2.3.1

Multiply $2$ by $0.6$ .

$x = - \frac{3}{1.2}$

Step 2.3.2

Divide $3$ by $1.2$ .

$x = - 1 \cdot 2.5$

Step 2.3.3

Multiply $- 1$ by $2.5$ .

$x = - 2.5$

Step 3

Evaluate $f (- 2.5)$ .

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Step 3.1

Replace the variable $x$ with $- 2.5$ in the expression.

$f (- 2.5) = 0.6 {(- 2.5)}^{2} + 3 (- 2.5) + 4$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Raise $- 2.5$ to the power of $2$ .

$f (- 2.5) = 0.6 \cdot 6.25 + 3 (- 2.5) + 4$

Step 3.2.1.2

Multiply $0.6$ by $6.25$ .

$f (- 2.5) = 3.75 + 3 (- 2.5) + 4$

Step 3.2.1.3

Multiply $3$ by $- 2.5$ .

$f (- 2.5) = 3.75 - 7.5 + 4$

Step 3.2.2

Simplify by adding and subtracting.

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Step 3.2.2.1

Subtract $7.5$ from $3.75$ .

$f (- 2.5) = - 3.75 + 4$

Step 3.2.2.2

Add $- 3.75$ and $4$ .

$f (- 2.5) = 0.25$

Step 3.2.3

The final answer is $0.25$ .

$0.25$

Step 4

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

$(- 2.5, 0.25)$

Step 5