Graph y=(-3x^2)/(2x+6)

$y = \frac{- 3 x^{2}}{2 x + 6}$

Step 1

Find the point at $x = - 2$ .

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = - \frac{3 {(- 2)}^{2}}{2 ((- 2) + 3)}$

Simplify the result.

Cancel the common factor of ${(- 2)}^{2}$ and $2$ .

Rewrite $- 2$ as $- 1 (2)$ .

$f (- 2) = - \frac{3 {(- 1 \cdot 2)}^{2}}{2 ((- 2) + 3)}$

Apply the product rule to $- 1 (2)$ .

$f (- 2) = - \frac{3 ({(- 1)}^{2} \cdot 2^{2})}{2 ((- 2) + 3)}$

Raise $- 1$ to the power of $2$ .

$f (- 2) = - \frac{3 (1 \cdot 2^{2})}{2 ((- 2) + 3)}$

Multiply $2^{2}$ by $1$ .

$f (- 2) = - \frac{3 \cdot 2^{2}}{2 ((- 2) + 3)}$

Factor $2$ out of $3 \cdot 2^{2}$ .

$f (- 2) = - \frac{2 (3 \cdot 2)}{2 (- 2 + 3)}$

Cancel the common factors.

Cancel the common factor.

$f (- 2) = - \frac{2 (3 \cdot 2)}{2 (- 2 + 3)}$

Rewrite the expression.

$f (- 2) = - \frac{3 \cdot 2}{- 2 + 3}$

Simplify the expression.

Multiply $3$ by $2$ .

$f (- 2) = - \frac{6}{- 2 + 3}$

Add $- 2$ and $3$ .

$f (- 2) = - \frac{6}{1}$

Divide $6$ by $1$ .

$f (- 2) = - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$f (- 2) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 2

Find the point at $x = 0$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = - \frac{3 {(0)}^{2}}{2 ((0) + 3)}$

Simplify the result.

Cancel the common factor of $3$ and $(0) + 3$ .

Factor $3$ out of $3 {(0)}^{2}$ .

$f (0) = - \frac{3 ({(0)}^{2})}{2 ((0) + 3)}$

Cancel the common factors.

Factor $3$ out of $2 ((0) + 3)$ .

$f (0) = - \frac{3 ({(0)}^{2})}{3 (2 (0 + 1))}$

Cancel the common factor.

$f (0) = - \frac{3 {(0)}^{2}}{3 (2 (0 + 1))}$

Rewrite the expression.

$f (0) = - \frac{{(0)}^{2}}{2 (0 + 1)}$

Simplify the expression.

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

$f (0) = - \frac{0}{2 (0 + 1)}$

Add $0$ and $1$ .

$f (0) = - \frac{0}{2 \cdot 1}$

Multiply $2$ by $1$ .

$f (0) = - \frac{0}{2}$

Divide $0$ by $2$ .

$f (0) = - 0$

Multiply $- 1$ by $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = - 1$ .

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = - \frac{3 {(- 1)}^{2}}{2 ((- 1) + 3)}$

Simplify the result.

Raise $- 1$ to the power of $2$ .

$f (- 1) = - \frac{3 \cdot 1}{2 (- 1 + 3)}$

Add $- 1$ and $3$ .

$f (- 1) = - \frac{3 \cdot 1}{2 \cdot 2}$

Multiply $3$ by $1$ .

$f (- 1) = - \frac{3}{2 \cdot 2}$

Multiply $2$ by $2$ .

$f (- 1) = - \frac{3}{4}$

The final answer is $- \frac{3}{4}$ .

$- \frac{3}{4}$

Convert $- \frac{3}{4}$ to decimal.

$y = - 0.75$

Step 4

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = - \frac{3 {(1)}^{2}}{2 ((1) + 3)}$

Simplify the result.

One to any power is one.

$f (1) = - \frac{3 \cdot 1}{2 (1 + 3)}$

Add $1$ and $3$ .

$f (1) = - \frac{3 \cdot 1}{2 \cdot 4}$

Multiply $3$ by $1$ .

$f (1) = - \frac{3}{2 \cdot 4}$

Multiply $2$ by $4$ .

$f (1) = - \frac{3}{8}$

The final answer is $- \frac{3}{8}$ .

$- \frac{3}{8}$

Convert $- \frac{3}{8}$ to decimal.

$y = - 0.375$

Step 5

Find the point at $x = 2$ .

Replace the variable $x$ with $2$ in the expression.

$f (2) = - \frac{3 {(2)}^{2}}{2 ((2) + 3)}$

Simplify the result.

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

Factor $2$ out of $3 {(2)}^{2}$ .

$f (2) = - \frac{2 (3 \cdot 2)}{2 ((2) + 3)}$

Cancel the common factors.

Cancel the common factor.

$f (2) = - \frac{2 (3 \cdot 2)}{2 ((2) + 3)}$

Rewrite the expression.

$f (2) = - \frac{3 \cdot 2}{(2) + 3}$

Simplify the expression.

Multiply $3$ by $2$ .

$f (2) = - \frac{6}{2 + 3}$

Add $2$ and $3$ .

$f (2) = - \frac{6}{5}$

The final answer is $- \frac{6}{5}$ .

$- \frac{6}{5}$

Convert $- \frac{6}{5}$ to decimal.

$y = - 1.2$

Step 6

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & - 0.75 \\ 0 & 0 \\ 1 & - 0.375 \\ 2 & - 1.2 \end{array}$

Step 7

The cubic function can be graphed using the function behavior and the selected points.

Not a polynomial

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & - 0.75 \\ 0 & 0 \\ 1 & - 0.375 \\ 2 & - 1.2 \end{array}$

Step 8

Graph y=(-3x^2)/(2x+6)

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