Find the Maximum/Minimum Value f(x)=-0.4x^2+2.7x+7

$f (x) = - 0.4 x^{2} + 2.7 x + 7$

Step 1

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

$f_{max}$ $x = a x^{2} + b x + c$ 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 $b$ .

$x = - \frac{2.7}{2 (- 0.4)}$

Remove parentheses.

$x = - \frac{2.7}{2 (- 0.4)}$

Simplify $- \frac{2.7}{2 (- 0.4)}$ .

Multiply $2$ by $- 0.4$ .

$x = - \frac{2.7}{- 0.8}$

Divide $2.7$ by $- 0.8$ .

$x = - - 3.375$

Multiply $- 1$ by $- 3.375$ .

$x = 3.375$

Step 3

Evaluate $f (3.375)$ .

Replace the variable $x$ with $3.375$ in the expression.

$f (3.375) = - 0.4 {(3.375)}^{2} + 2.7 (3.375) + 7$

Simplify the result.

Simplify each term.

Raise $3.375$ to the power of $2$ .

$f (3.375) = - 0.4 \cdot 11.390625 + 2.7 (3.375) + 7$

Multiply $- 0.4$ by $11.390625$ .

$f (3.375) = - 4.55625 + 2.7 (3.375) + 7$

Multiply $2.7$ by $3.375$ .

$f (3.375) = - 4.55625 + 9.1125 + 7$

Simplify by adding numbers.

Add $- 4.55625$ and $9.1125$ .

$f (3.375) = 4.55625 + 7$

Add $4.55625$ and $7$ .

$f (3.375) = 11.55625$

The final answer is $11.55625$ .

$11.55625$

Step 4

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

$(3.375, 11.55625)$

Step 5

Find the Maximum/Minimum Value f(x)=-0.4x^2+2.7x+7

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