Find the Maximum/Minimum Value h(t)=-16t^2+704t

$h (t) = - 16 t^{2} + 704 t$

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 $f (- \frac{b}{2 a})$ .

$f_{max}$ $t = a t^{2} + b t + c$ occurs at $t = - \frac{b}{2 a}$

Step 2

Find the value of $t = - \frac{b}{2 a}$ .

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

$t = - \frac{704}{2 (- 16)}$

Remove parentheses.

$t = - \frac{704}{2 (- 16)}$

Simplify $- \frac{704}{2 (- 16)}$ .

Cancel the common factor of $704$ and $2$ .

Factor $2$ out of $704$ .

$t = - \frac{2 \cdot 352}{2 \cdot - 16}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 16$ .

$t = - \frac{2 \cdot 352}{2 (- 16)}$

Cancel the common factor.

$t = - \frac{2 \cdot 352}{2 \cdot - 16}$

Rewrite the expression.

$t = - \frac{352}{- 16}$

Cancel the common factor of $352$ and $- 16$ .

Factor $16$ out of $352$ .

$t = - \frac{16 (22)}{- 16}$

Move the negative one from the denominator of $\frac{22}{- 1}$ .

$t = - (- 1 \cdot 22)$

Multiply $- (- 1 \cdot 22)$ .

Multiply $- 1$ by $22$ .

$t = - - 22$

Multiply $- 1$ by $- 22$ .

$t = 22$

Step 3

Evaluate $f (22)$ .

Replace the variable $t$ with $22$ in the expression.

$h (22) = - 16 {(22)}^{2} + 704 (22)$

Simplify the result.

Simplify each term.

Raise $22$ to the power of $2$ .

$h (22) = - 16 \cdot 484 + 704 (22)$

Multiply $- 16$ by $484$ .

$h (22) = - 7744 + 704 (22)$

Multiply $704$ by $22$ .

$h (22) = - 7744 + 15488$

Add $- 7744$ and $15488$ .

$h (22) = 7744$

The final answer is $7744$ .

$7744$

Step 4

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

$(22, 7744)$

Step 5

Find the Maximum/Minimum Value h(t)=-16t^2+704t

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