Find the Vertex Form y=2(x-3)(x+5)

$y = 2 (x - 3) (x + 5)$

Step 1

Complete the square for $2 (x - 3) (x + 5)$ .

Simplify the expression.

Apply the distributive property.

$(2 x + 2 \cdot - 3) (x + 5)$

Multiply $2$ by $- 3$ .

$(2 x - 6) (x + 5)$

Expand $(2 x - 6) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$2 x (x + 5) - 6 (x + 5)$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 5 - 6 (x + 5)$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 5 - 6 x - 6 \cdot 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 5 - 6 x - 6 \cdot 5$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 5 - 6 x - 6 \cdot 5$

Multiply $5$ by $2$ .

$2 x^{2} + 10 x - 6 x - 6 \cdot 5$

Multiply $- 6$ by $5$ .

$2 x^{2} + 10 x - 6 x - 30$

Subtract $6 x$ from $10 x$ .

$2 x^{2} + 4 x - 30$

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

$a = 2$

$b = 4$

$c = - 30$

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

$d = \frac{4}{2 \cdot 2}$

Simplify the right side.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$d = \frac{2}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d = \frac{2}{2}$

Rewrite the expression.

$d = 1$

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

$e = - 30 - \frac{4^{2}}{4 \cdot 2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4^{2}$ and $4$ .

Factor $4$ out of $4^{2}$ .

$e = - 30 - \frac{4 \cdot 4}{4 \cdot 2}$

Cancel the common factors.

Factor $4$ out of $4 \cdot 2$ .

$e = - 30 - \frac{4 \cdot 4}{4 (2)}$

Cancel the common factor.

$e = - 30 - \frac{4 \cdot 4}{4 \cdot 2}$

Rewrite the expression.

$e = - 30 - \frac{4}{2}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4$ .

$e = - 30 - \frac{2 \cdot 2}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$e = - 30 - \frac{2 \cdot 2}{2 (1)}$

Cancel the common factor.

$e = - 30 - \frac{2 \cdot 2}{2 \cdot 1}$

Rewrite the expression.

$e = - 30 - \frac{2}{1}$

Divide $2$ by $1$ .

$e = - 30 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$e = - 30 - 2$

Subtract $2$ from $- 30$ .

$e = - 32$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $2 {(x + 1)}^{2} - 32$ .

$2 {(x + 1)}^{2} - 32$

Step 2

Set $y$ equal to the new right side.

$y = 2 {(x + 1)}^{2} - 32$

Find the Vertex Form y=2(x-3)(x+5)

Related Questions

Support LCMGCF.com by disabling your adblocker.