Find the Vertex Form y=-3x^2+48x

$y = - 3 x^{2} + 48 x$

Step 1

Complete the square for $- 3 x^{2} + 48 x$ .

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

$a = - 3$

$b = 48$

$c = 0$

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

$d = \frac{48}{2 \cdot - 3}$

Simplify the right side.

Cancel the common factor of $48$ and $2$ .

Factor $2$ out of $48$ .

$d = \frac{2 \cdot 24}{2 \cdot - 3}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 3$ .

$d = \frac{2 \cdot 24}{2 (- 3)}$

Cancel the common factor.

$d = \frac{2 \cdot 24}{2 \cdot - 3}$

Rewrite the expression.

$d = \frac{24}{- 3}$

Cancel the common factor of $24$ and $- 3$ .

Factor $3$ out of $24$ .

$d = \frac{3 (8)}{- 3}$

Move the negative one from the denominator of $\frac{8}{- 1}$ .

$d = - 1 \cdot 8$

Multiply $- 1$ by $8$ .

$d = - 8$

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

$e = 0 - \frac{48^{2}}{4 \cdot - 3}$

Simplify the right side.

Simplify each term.

Raise $48$ to the power of $2$ .

$e = 0 - \frac{2304}{4 \cdot - 3}$

Multiply $4$ by $- 3$ .

$e = 0 - \frac{2304}{- 12}$

Divide $2304$ by $- 12$ .

$e = 0 - - 192$

Multiply $- 1$ by $- 192$ .

$e = 0 + 192$

Add $0$ and $192$ .

$e = 192$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $- 3 {(x - 8)}^{2} + 192$ .

$- 3 {(x - 8)}^{2} + 192$

Step 2

Set $y$ equal to the new right side.

$y = - 3 {(x - 8)}^{2} + 192$

Find the Vertex Form y=-3x^2+48x

Related Questions

Support LCMGCF.com by disabling your adblocker.