Find the Vertex Form y=5x^2+12x^2-20

$y = 5 x^{2} + 12 x^{2} - 20$

Step 1

Add $5 x^{2}$ and $12 x^{2}$ .

$y = 17 x^{2} - 20$

Step 2

Complete the square for $17 x^{2} - 20$ .

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

$a = 17$

$b = 0$

$c = - 20$

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

$d = \frac{0}{2 \cdot 17}$

Simplify the right side.

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $0$ .

$d = \frac{2 (0)}{2 \cdot 17}$

Cancel the common factors.

Factor $2$ out of $2 \cdot 17$ .

$d = \frac{2 (0)}{2 (17)}$

Cancel the common factor.

$d = \frac{2 \cdot 0}{2 \cdot 17}$

Rewrite the expression.

$d = \frac{0}{17}$

Cancel the common factor of $0$ and $17$ .

Factor $17$ out of $0$ .

$d = \frac{17 (0)}{17}$

Cancel the common factors.

Factor $17$ out of $17$ .

$d = \frac{17 \cdot 0}{17 \cdot 1}$

Cancel the common factor.

$d = \frac{17 \cdot 0}{17 \cdot 1}$

Rewrite the expression.

$d = \frac{0}{1}$

Divide $0$ by $1$ .

$d = 0$

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

$e = - 20 - \frac{0^{2}}{4 \cdot 17}$

Simplify the right side.

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$e = - 20 - \frac{0}{4 \cdot 17}$

Multiply $4$ by $17$ .

$e = - 20 - \frac{0}{68}$

Divide $0$ by $68$ .

$e = - 20 - 0$

Multiply $- 1$ by $0$ .

$e = - 20 + 0$

Add $- 20$ and $0$ .

$e = - 20$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $17 {(x + 0)}^{2} - 20$ .

$17 {(x + 0)}^{2} - 20$

Step 3

Set $y$ equal to the new right side.

$y = 17 {(x + 0)}^{2} - 20$

Find the Vertex Form y=5x^2+12x^2-20

Related Questions

Support LCMGCF.com by disabling your adblocker.