Write in Standard Form x=-y^2+16y-69

$x = - y^{2} + 16 y - 69$

Solve for $y$ .

Rewrite the equation as $- y^{2} + 16 y - 69 = x$ .

$- y^{2} + 16 y - 69 = x$

Subtract $x$ from both sides of the equation.

$- y^{2} + 16 y - 69 - x = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 1$ , $b = 16$ , and $c = - 69 - x$ into the quadratic formula and solve for $y$ .

$\frac{- 16 \pm \sqrt{16^{2} - 4 \cdot (- 1 \cdot (- 69 - x))}}{2 \cdot - 1}$

Simplify.

Simplify the numerator.

Raise $16$ to the power of $2$ .

$y = \frac{- 16 \pm \sqrt{256 - 4 \cdot - 1 \cdot (- 69 - x)}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$y = \frac{- 16 \pm \sqrt{256 + 4 \cdot (- 69 - x)}}{2 \cdot - 1}$

Apply the distributive property.

$y = \frac{- 16 \pm \sqrt{256 + 4 \cdot - 69 + 4 (- x)}}{2 \cdot - 1}$

Multiply $4$ by $- 69$ .

$y = \frac{- 16 \pm \sqrt{256 - 276 + 4 (- x)}}{2 \cdot - 1}$

Multiply $- 1$ by $4$ .

$y = \frac{- 16 \pm \sqrt{256 - 276 - 4 x}}{2 \cdot - 1}$

Subtract $276$ from $256$ .

$y = \frac{- 16 \pm \sqrt{- 20 - 4 x}}{2 \cdot - 1}$

Factor $4$ out of $- 20 - 4 x$ .

Factor $4$ out of $- 20$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5) - 4 x}}{2 \cdot - 1}$

Factor $4$ out of $- 4 x$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5) + 4 (- x)}}{2 \cdot - 1}$

Factor $4$ out of $4 (- 5) + 4 (- x)$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5 - x)}}{2 \cdot - 1}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 16 \pm \sqrt{2^{2} (- 5 - x)}}{2 \cdot - 1}$

Pull terms out from under the radical.

$y = \frac{- 16 \pm 2 \sqrt{- 5 - x}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$y = \frac{- 16 \pm 2 \sqrt{- 5 - x}}{- 2}$

Simplify $\frac{- 16 \pm 2 \sqrt{- 5 - x}}{- 2}$ .

$y = 8 \pm \sqrt{- 5 - x}$

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

Simplify the numerator.

Raise $16$ to the power of $2$ .

$y = \frac{- 16 \pm \sqrt{256 - 4 \cdot - 1 \cdot (- 69 - x)}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$y = \frac{- 16 \pm \sqrt{256 + 4 \cdot (- 69 - x)}}{2 \cdot - 1}$

Apply the distributive property.

$y = \frac{- 16 \pm \sqrt{256 + 4 \cdot - 69 + 4 (- x)}}{2 \cdot - 1}$

Multiply $4$ by $- 69$ .

$y = \frac{- 16 \pm \sqrt{256 - 276 + 4 (- x)}}{2 \cdot - 1}$

Multiply $- 1$ by $4$ .

$y = \frac{- 16 \pm \sqrt{256 - 276 - 4 x}}{2 \cdot - 1}$

Subtract $276$ from $256$ .

$y = \frac{- 16 \pm \sqrt{- 20 - 4 x}}{2 \cdot - 1}$

Factor $4$ out of $- 20 - 4 x$ .

Factor $4$ out of $- 20$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5) - 4 x}}{2 \cdot - 1}$

Factor $4$ out of $- 4 x$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5) + 4 (- x)}}{2 \cdot - 1}$

Factor $4$ out of $4 (- 5) + 4 (- x)$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5 - x)}}{2 \cdot - 1}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 16 \pm \sqrt{2^{2} (- 5 - x)}}{2 \cdot - 1}$

Pull terms out from under the radical.

$y = \frac{- 16 \pm 2 \sqrt{- 5 - x}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$y = \frac{- 16 \pm 2 \sqrt{- 5 - x}}{- 2}$

Simplify $\frac{- 16 \pm 2 \sqrt{- 5 - x}}{- 2}$ .

$y = 8 \pm \sqrt{- 5 - x}$

Change the $\pm$ to $+$ .

$y = 8 + \sqrt{- 5 - x}$

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

Simplify the numerator.

Raise $16$ to the power of $2$ .

$y = \frac{- 16 \pm \sqrt{256 - 4 \cdot - 1 \cdot (- 69 - x)}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$y = \frac{- 16 \pm \sqrt{256 + 4 \cdot (- 69 - x)}}{2 \cdot - 1}$

Apply the distributive property.

$y = \frac{- 16 \pm \sqrt{256 + 4 \cdot - 69 + 4 (- x)}}{2 \cdot - 1}$

Multiply $4$ by $- 69$ .

$y = \frac{- 16 \pm \sqrt{256 - 276 + 4 (- x)}}{2 \cdot - 1}$

Multiply $- 1$ by $4$ .

$y = \frac{- 16 \pm \sqrt{256 - 276 - 4 x}}{2 \cdot - 1}$

Subtract $276$ from $256$ .

$y = \frac{- 16 \pm \sqrt{- 20 - 4 x}}{2 \cdot - 1}$

Factor $4$ out of $- 20 - 4 x$ .

Factor $4$ out of $- 20$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5) - 4 x}}{2 \cdot - 1}$

Factor $4$ out of $- 4 x$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5) + 4 (- x)}}{2 \cdot - 1}$

Factor $4$ out of $4 (- 5) + 4 (- x)$ .

$y = \frac{- 16 \pm \sqrt{4 (- 5 - x)}}{2 \cdot - 1}$

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 16 \pm \sqrt{2^{2} (- 5 - x)}}{2 \cdot - 1}$

Pull terms out from under the radical.

$y = \frac{- 16 \pm 2 \sqrt{- 5 - x}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$y = \frac{- 16 \pm 2 \sqrt{- 5 - x}}{- 2}$

Simplify $\frac{- 16 \pm 2 \sqrt{- 5 - x}}{- 2}$ .

$y = 8 \pm \sqrt{- 5 - x}$

Change the $\pm$ to $-$ .

$y = 8 - \sqrt{- 5 - x}$

The final answer is the combination of both solutions.

$y = 8 + \sqrt{- 5 - x}$

$y = 8 - \sqrt{- 5 - x}$

$y = 8 + \sqrt{- 5 - x}$

$y = 8 - \sqrt{- 5 - x}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

The standard form is $8 + \sqrt{- 5 - x}, 8 - \sqrt{- 5 - x}$ .

$y = 8 + \sqrt{- 5 - x}$

$y = 8 - \sqrt{- 5 - x}$

Write in Standard Form x=-y^2+16y-69

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