Find the Vertex -x^2+50x-264

$- x^{2} + 50 x - 264$

Step 1

Rewrite the equation in vertex form.

Complete the square for $- x^{2} + 50 x - 264$ .

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = - 1$

$b = 50$

$c = - 264$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{50}{2 \cdot - 1}$

Simplify the right side.

Cancel the common factor of $50$ and $2$ .

Factor $2$ out of $50$ .

$d = \frac{2 \cdot 25}{2 \cdot - 1}$

Move the negative one from the denominator of $\frac{25}{- 1}$ .

$d = - 1 \cdot 25$

Multiply $- 1$ by $25$ .

$d = - 25$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = - 264 - \frac{50^{2}}{4 \cdot - 1}$

Simplify the right side.

Simplify each term.

Raise $50$ to the power of $2$ .

$e = - 264 - \frac{2500}{4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$e = - 264 - \frac{2500}{- 4}$

Divide $2500$ by $- 4$ .

$e = - 264 - - 625$

Multiply $- 1$ by $- 625$ .

$e = - 264 + 625$

Add $- 264$ and $625$ .

$e = 361$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $- {(x - 25)}^{2} + 361$ .

$- {(x - 25)}^{2} + 361$

Set $y$ equal to the new right side.

$y = - {(x - 25)}^{2} + 361$

Step 2

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = - 1$

$h = 25$

$k = 361$

Step 3

Find the vertex $(h, k)$ .

$(25, 361)$

Step 4

Find the Vertex -x^2+50x-264

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