Graph y=2x^3+x^2-7x-6

$y = 2 x^{3} + x^{2} - 7 x - 6$

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = 2 {(- 2)}^{3} + {(- 2)}^{2} - 7 \cdot - 2 - 6$

Simplify the result.

Simplify each term.

Raise $- 2$ to the power of $3$ .

$f (- 2) = 2 \cdot - 8 + {(- 2)}^{2} - 7 \cdot - 2 - 6$

Multiply $2$ by $- 8$ .

$f (- 2) = - 16 + {(- 2)}^{2} - 7 \cdot - 2 - 6$

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

$f (- 2) = - 16 + 4 - 7 \cdot - 2 - 6$

Multiply $- 7$ by $- 2$ .

$f (- 2) = - 16 + 4 + 14 - 6$

Simplify by adding and subtracting.

Add $- 16$ and $4$ .

$f (- 2) = - 12 + 14 - 6$

Add $- 12$ and $14$ .

$f (- 2) = 2 - 6$

Subtract $6$ from $2$ .

$f (- 2) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} + {(- 1)}^{2} - 7 \cdot - 1 - 6$

Simplify the result.

Simplify each term.

Raise $- 1$ to the power of $3$ .

$f (- 1) = 2 \cdot - 1 + {(- 1)}^{2} - 7 \cdot - 1 - 6$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 + {(- 1)}^{2} - 7 \cdot - 1 - 6$

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

$f (- 1) = - 2 + 1 - 7 \cdot - 1 - 6$

Multiply $- 7$ by $- 1$ .

$f (- 1) = - 2 + 1 + 7 - 6$

Simplify by adding and subtracting.

Add $- 2$ and $1$ .

$f (- 1) = - 1 + 7 - 6$

Add $- 1$ and $7$ .

$f (- 1) = 6 - 6$

Subtract $6$ from $6$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 0$ .

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

$f (0) = 2 {(0)}^{3} + {(0)}^{2} - 7 \cdot 0 - 6$

Simplify the result.

Simplify each term.

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

$f (0) = 2 \cdot 0 + {(0)}^{2} - 7 \cdot 0 - 6$

Multiply $2$ by $0$ .

$f (0) = 0 + {(0)}^{2} - 7 \cdot 0 - 6$

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

$f (0) = 0 + 0 - 7 \cdot 0 - 6$

Multiply $- 7$ by $0$ .

$f (0) = 0 + 0 + 0 - 6$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 + 0 - 6$

Add $0$ and $0$ .

$f (0) = 0 - 6$

Subtract $6$ from $0$ .

$f (0) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 4

Find the point at $x = 1$ .

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

$f (1) = 2 {(1)}^{3} + {(1)}^{2} - 7 \cdot 1 - 6$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 2 \cdot 1 + {(1)}^{2} - 7 \cdot 1 - 6$

Multiply $2$ by $1$ .

$f (1) = 2 + {(1)}^{2} - 7 \cdot 1 - 6$

One to any power is one.

$f (1) = 2 + 1 - 7 \cdot 1 - 6$

Multiply $- 7$ by $1$ .

$f (1) = 2 + 1 - 7 - 6$

Simplify by adding and subtracting.

Add $2$ and $1$ .

$f (1) = 3 - 7 - 6$

Subtract $7$ from $3$ .

$f (1) = - 4 - 6$

Subtract $6$ from $- 4$ .

$f (1) = - 10$

The final answer is $- 10$ .

$- 10$

Convert $- 10$ to decimal.

$y = - 10$

Step 5

Find the point at $x = 2$ .

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

$f (2) = 2 {(2)}^{3} + {(2)}^{2} - 7 \cdot 2 - 6$

Simplify the result.

Simplify each term.

Multiply $2$ by ${(2)}^{3}$ by adding the exponents.

Multiply $2$ by ${(2)}^{3}$ .

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

$f (2) = 2 {(2)}^{3} + {(2)}^{2} - 7 \cdot 2 - 6$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 2^{1 + 3} + {(2)}^{2} - 7 \cdot 2 - 6$

Add $1$ and $3$ .

$f (2) = 2^{4} + {(2)}^{2} - 7 \cdot 2 - 6$

Raise $2$ to the power of $4$ .

$f (2) = 16 + {(2)}^{2} - 7 \cdot 2 - 6$

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

$f (2) = 16 + 4 - 7 \cdot 2 - 6$

Multiply $- 7$ by $2$ .

$f (2) = 16 + 4 - 14 - 6$

Simplify by adding and subtracting.

Add $16$ and $4$ .

$f (2) = 20 - 14 - 6$

Subtract $14$ from $20$ .

$f (2) = 6 - 6$

Subtract $6$ from $6$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 4 \\ - 1 & 0 \\ 0 & - 6 \\ 1 & - 10 \\ 2 & 0 \end{array}$

Step 7

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 2 & - 4 \\ - 1 & 0 \\ 0 & - 6 \\ 1 & - 10 \\ 2 & 0 \end{array}$

Step 8

Graph y=2x^3+x^2-7x-6

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