Find the Maximum/Minimum Value -4.9x^2+19.6x+24.5

$- 4.9 x^{2} + 19.6 x + 24.5$

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 $b$ .

$x = - \frac{19.6}{2 (- 4.9)}$

Remove parentheses.

$x = - \frac{19.6}{2 (- 4.9)}$

Simplify $- \frac{19.6}{2 (- 4.9)}$ .

Multiply $2$ by $- 4.9$ .

$x = - \frac{19.6}{- 9.8}$

Divide $19.6$ by $- 9.8$ .

$x = - - 2$

Multiply $- 1$ by $- 2$ .

$x = 2$

Step 3

Evaluate $f (2)$ .

Replace the variable $x$ with $2$ in the expression.

$f (2) = - 4.9 {(2)}^{2} + 19.6 (2) + 24.5$

Simplify the result.

Simplify each term.

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

$f (2) = - 4.9 \cdot 4 + 19.6 (2) + 24.5$

Multiply $- 4.9$ by $4$ .

$f (2) = - 19.6 + 19.6 (2) + 24.5$

Multiply $19.6$ by $2$ .

$f (2) = - 19.6 + 39.2 + 24.5$

Simplify by adding numbers.

Add $- 19.6$ and $39.2$ .

$f (2) = 19.6 + 24.5$

Add $19.6$ and $24.5$ .

$f (2) = 44.1$

The final answer is $44.1$ .

$44.1$

Step 4

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

$(2, 44.1)$

Step 5

Find the Maximum/Minimum Value -4.9x^2+19.6x+24.5

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