Graph f(x)=2x^3-26x-24

$f (x) = 2 x^{3} - 26 x - 24$

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = 2 {(- 2)}^{3} - 26 \cdot - 2 - 24$

Simplify the result.

Simplify each term.

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

$f (- 2) = 2 \cdot - 8 - 26 \cdot - 2 - 24$

Multiply $2$ by $- 8$ .

$f (- 2) = - 16 - 26 \cdot - 2 - 24$

Multiply $- 26$ by $- 2$ .

$f (- 2) = - 16 + 52 - 24$

Simplify by adding and subtracting.

Add $- 16$ and $52$ .

$f (- 2) = 36 - 24$

Subtract $24$ from $36$ .

$f (- 2) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} - 26 \cdot - 1 - 24$

Simplify the result.

Simplify each term.

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

$f (- 1) = 2 \cdot - 1 - 26 \cdot - 1 - 24$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 - 26 \cdot - 1 - 24$

Multiply $- 26$ by $- 1$ .

$f (- 1) = - 2 + 26 - 24$

Simplify by adding and subtracting.

Add $- 2$ and $26$ .

$f (- 1) = 24 - 24$

Subtract $24$ from $24$ .

$f (- 1) = 0$

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.

$f (0) = 2 {(0)}^{3} - 26 \cdot 0 - 24$

Simplify the result.

Simplify each term.

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

$f (0) = 2 \cdot 0 - 26 \cdot 0 - 24$

Multiply $2$ by $0$ .

$f (0) = 0 - 26 \cdot 0 - 24$

Multiply $- 26$ by $0$ .

$f (0) = 0 + 0 - 24$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 - 24$

Subtract $24$ from $0$ .

$f (0) = - 24$

The final answer is $- 24$ .

$- 24$

Convert $- 24$ to decimal.

$y = - 24$

Step 4

Find the point at $x = 1$ .

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

$f (1) = 2 {(1)}^{3} - 26 \cdot 1 - 24$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 2 \cdot 1 - 26 \cdot 1 - 24$

Multiply $2$ by $1$ .

$f (1) = 2 - 26 \cdot 1 - 24$

Multiply $- 26$ by $1$ .

$f (1) = 2 - 26 - 24$

Simplify by subtracting numbers.

Subtract $26$ from $2$ .

$f (1) = - 24 - 24$

Subtract $24$ from $- 24$ .

$f (1) = - 48$

The final answer is $- 48$ .

$- 48$

Convert $- 48$ to decimal.

$y = - 48$

Step 5

Find the point at $x = 2$ .

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

$f (2) = 2 {(2)}^{3} - 26 \cdot 2 - 24$

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 $1$ .

$f (2) = 2 {(2)}^{3} - 26 \cdot 2 - 24$

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

$f (2) = 2^{1 + 3} - 26 \cdot 2 - 24$

Add $1$ and $3$ .

$f (2) = 2^{4} - 26 \cdot 2 - 24$

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

$f (2) = 16 - 26 \cdot 2 - 24$

Multiply $- 26$ by $2$ .

$f (2) = 16 - 52 - 24$

Simplify by subtracting numbers.

Subtract $52$ from $16$ .

$f (2) = - 36 - 24$

Subtract $24$ from $- 36$ .

$f (2) = - 60$

The final answer is $- 60$ .

$- 60$

Convert $- 60$ to decimal.

$y = - 60$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & 0 \\ 0 & - 24 \\ 1 & - 48 \\ 2 & - 60 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & 12 \\ - 1 & 0 \\ 0 & - 24 \\ 1 & - 48 \\ 2 & - 60 \end{array}$

Step 8

Graph f(x)=2x^3-26x-24

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