Find the Vertex -5x^2+280x-3675

$- 5 x^{2} + 280 x - 3675$

Step 1

Rewrite the equation in vertex form.

Complete the square for $- 5 x^{2} + 280 x - 3675$ .

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

$a = - 5$

$b = 280$

$c = - 3675$

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 $d = \frac{b}{2 a}$ .

$d = \frac{280}{2 \cdot - 5}$

Simplify the right side.

Cancel the common factor of $280$ and $2$ .

Factor $2$ out of $280$ .

$d = \frac{2 \cdot 140}{2 \cdot - 5}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 5$ .

$d = \frac{2 \cdot 140}{2 (- 5)}$

Cancel the common factor.

$d = \frac{2 \cdot 140}{2 \cdot - 5}$

Rewrite the expression.

$d = \frac{140}{- 5}$

Cancel the common factor of $140$ and $- 5$ .

Factor $5$ out of $140$ .

$d = \frac{5 (28)}{- 5}$

Move the negative one from the denominator of $\frac{28}{- 1}$ .

$d = - 1 \cdot 28$

Multiply $- 1$ by $28$ .

$d = - 28$

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 $e = c - \frac{b^{2}}{4 a}$ .

$e = - 3675 - \frac{280^{2}}{4 \cdot - 5}$

Simplify the right side.

Simplify each term.

Raise $280$ to the power of $2$ .

$e = - 3675 - \frac{78400}{4 \cdot - 5}$

Multiply $4$ by $- 5$ .

$e = - 3675 - \frac{78400}{- 20}$

Divide $78400$ by $- 20$ .

$e = - 3675 - - 3920$

Multiply $- 1$ by $- 3920$ .

$e = - 3675 + 3920$

Add $- 3675$ and $3920$ .

$e = 245$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $- 5 {(x - 28)}^{2} + 245$ .

$- 5 {(x - 28)}^{2} + 245$

Set $y$ equal to the new right side.

$y = - 5 {(x - 28)}^{2} + 245$

Step 2

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

$a = - 5$

$h = 28$

$k = 245$

Step 3

Find the vertex $(h, k)$ .

$(28, 245)$

Step 4

Find the Vertex -5x^2+280x-3675

Related Questions

Support LCMGCF.com by disabling your adblocker.