Write as a Function of h h=-16t^2+56t

$h = - 16 t^{2} + 56 t$

Rewrite the equation as $- 16 t^{2} + 56 t = h$ .

$- 16 t^{2} + 56 t = h$

Subtract $h$ from both sides of the equation.

$- 16 t^{2} + 56 t - h = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = - 16$ , $b = 56$ , and $c = - h$ into the quadratic formula and solve for $t$ .

$\frac{- 56 \pm \sqrt{56^{2} - 4 \cdot (- 16 \cdot (- h))}}{2 \cdot - 16}$

Simplify.

Simplify the numerator.

Raise $56$ to the power of $2$ .

$t = \frac{- 56 \pm \sqrt{3136 - 4 \cdot - 16 \cdot (- 1 h)}}{2 \cdot - 16}$

Multiply $- 4$ by $- 16$ .

$t = \frac{- 56 \pm \sqrt{3136 + 64 \cdot (- 1 h)}}{2 \cdot - 16}$

Multiply $64$ by $- 1$ .

$t = \frac{- 56 \pm \sqrt{3136 - 64 h}}{2 \cdot - 16}$

Factor $64$ out of $3136 - 64 h$ .

Factor $64$ out of $3136$ .

$t = \frac{- 56 \pm \sqrt{64 (49) - 64 h}}{2 \cdot - 16}$

Factor $64$ out of $- 64 h$ .

$t = \frac{- 56 \pm \sqrt{64 (49) + 64 (- h)}}{2 \cdot - 16}$

Factor $64$ out of $64 (49) + 64 (- h)$ .

$t = \frac{- 56 \pm \sqrt{64 (49 - h)}}{2 \cdot - 16}$

Rewrite $64 (49 - h)$ as $8^{2} (7^{2} - h)$ .

Rewrite $64$ as $8^{2}$ .

$t = \frac{- 56 \pm \sqrt{8^{2} (49 - h)}}{2 \cdot - 16}$

Rewrite $49$ as $7^{2}$ .

$t = \frac{- 56 \pm \sqrt{8^{2} (7^{2} - h)}}{2 \cdot - 16}$

Pull terms out from under the radical.

$t = \frac{- 56 \pm 8 \sqrt{7^{2} - h}}{2 \cdot - 16}$

Raise $7$ to the power of $2$ .

$t = \frac{- 56 \pm 8 \sqrt{49 - h}}{2 \cdot - 16}$

Multiply $2$ by $- 16$ .

$t = \frac{- 56 \pm 8 \sqrt{49 - h}}{- 32}$

Simplify $\frac{- 56 \pm 8 \sqrt{49 - h}}{- 32}$ .

$t = \frac{7 \pm \sqrt{49 - h}}{4}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $56$ to the power of $2$ .

$t = \frac{- 56 \pm \sqrt{3136 - 4 \cdot - 16 \cdot (- 1 h)}}{2 \cdot - 16}$

Multiply $- 4$ by $- 16$ .

$t = \frac{- 56 \pm \sqrt{3136 + 64 \cdot (- 1 h)}}{2 \cdot - 16}$

Multiply $64$ by $- 1$ .

$t = \frac{- 56 \pm \sqrt{3136 - 64 h}}{2 \cdot - 16}$

Factor $64$ out of $3136 - 64 h$ .

Factor $64$ out of $3136$ .

$t = \frac{- 56 \pm \sqrt{64 (49) - 64 h}}{2 \cdot - 16}$

Factor $64$ out of $- 64 h$ .

$t = \frac{- 56 \pm \sqrt{64 (49) + 64 (- h)}}{2 \cdot - 16}$

Factor $64$ out of $64 (49) + 64 (- h)$ .

$t = \frac{- 56 \pm \sqrt{64 (49 - h)}}{2 \cdot - 16}$

Rewrite $64 (49 - h)$ as $8^{2} (7^{2} - h)$ .

Rewrite $64$ as $8^{2}$ .

$t = \frac{- 56 \pm \sqrt{8^{2} (49 - h)}}{2 \cdot - 16}$

Rewrite $49$ as $7^{2}$ .

$t = \frac{- 56 \pm \sqrt{8^{2} (7^{2} - h)}}{2 \cdot - 16}$

Pull terms out from under the radical.

$t = \frac{- 56 \pm 8 \sqrt{7^{2} - h}}{2 \cdot - 16}$

Raise $7$ to the power of $2$ .

$t = \frac{- 56 \pm 8 \sqrt{49 - h}}{2 \cdot - 16}$

Multiply $2$ by $- 16$ .

$t = \frac{- 56 \pm 8 \sqrt{49 - h}}{- 32}$

Simplify $\frac{- 56 \pm 8 \sqrt{49 - h}}{- 32}$ .

$t = \frac{7 \pm \sqrt{49 - h}}{4}$

Change the $\pm$ to $+$ .

$t = \frac{7 + \sqrt{49 - h}}{4}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $56$ to the power of $2$ .

$t = \frac{- 56 \pm \sqrt{3136 - 4 \cdot - 16 \cdot (- 1 h)}}{2 \cdot - 16}$

Multiply $- 4$ by $- 16$ .

$t = \frac{- 56 \pm \sqrt{3136 + 64 \cdot (- 1 h)}}{2 \cdot - 16}$

Multiply $64$ by $- 1$ .

$t = \frac{- 56 \pm \sqrt{3136 - 64 h}}{2 \cdot - 16}$

Factor $64$ out of $3136 - 64 h$ .

Factor $64$ out of $3136$ .

$t = \frac{- 56 \pm \sqrt{64 (49) - 64 h}}{2 \cdot - 16}$

Factor $64$ out of $- 64 h$ .

$t = \frac{- 56 \pm \sqrt{64 (49) + 64 (- h)}}{2 \cdot - 16}$

Factor $64$ out of $64 (49) + 64 (- h)$ .

$t = \frac{- 56 \pm \sqrt{64 (49 - h)}}{2 \cdot - 16}$

Rewrite $64 (49 - h)$ as $8^{2} (7^{2} - h)$ .

Rewrite $64$ as $8^{2}$ .

$t = \frac{- 56 \pm \sqrt{8^{2} (49 - h)}}{2 \cdot - 16}$

Rewrite $49$ as $7^{2}$ .

$t = \frac{- 56 \pm \sqrt{8^{2} (7^{2} - h)}}{2 \cdot - 16}$

Pull terms out from under the radical.

$t = \frac{- 56 \pm 8 \sqrt{7^{2} - h}}{2 \cdot - 16}$

Raise $7$ to the power of $2$ .

$t = \frac{- 56 \pm 8 \sqrt{49 - h}}{2 \cdot - 16}$

Multiply $2$ by $- 16$ .

$t = \frac{- 56 \pm 8 \sqrt{49 - h}}{- 32}$

Simplify $\frac{- 56 \pm 8 \sqrt{49 - h}}{- 32}$ .

$t = \frac{7 \pm \sqrt{49 - h}}{4}$

Change the $\pm$ to $-$ .

$t = \frac{7 - \sqrt{49 - h}}{4}$

The final answer is the combination of both solutions.

$t = \frac{7 + \sqrt{49 - h}}{4}$

$t = \frac{7 - \sqrt{49 - h}}{4}$

Write as a Function of h h=-16t^2+56t

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