Graph P(x)=15x^3-3x^2+x+4

$P (x) = 15 x^{3} - 3 x^{2} + x + 4$

Step 1

Find the point at $x = - 1$ .

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

$f (- 1) = 15 {(- 1)}^{3} - 3 {(- 1)}^{2} - 1 + 4$

Simplify the result.

Remove parentheses.

$f (- 1) = 15 {(- 1)}^{3} - 3 {(- 1)}^{2} - 1 + 4$

Simplify each term.

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

$f (- 1) = 15 \cdot - 1 - 3 {(- 1)}^{2} - 1 + 4$

Multiply $15$ by $- 1$ .

$f (- 1) = - 15 - 3 {(- 1)}^{2} - 1 + 4$

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

$f (- 1) = - 15 - 3 \cdot 1 - 1 + 4$

Multiply $- 3$ by $1$ .

$f (- 1) = - 15 - 3 - 1 + 4$

Simplify by adding and subtracting.

Subtract $3$ from $- 15$ .

$f (- 1) = - 18 - 1 + 4$

Subtract $1$ from $- 18$ .

$f (- 1) = - 19 + 4$

Add $- 19$ and $4$ .

$f (- 1) = - 15$

The final answer is $- 15$ .

$- 15$

Convert $- 15$ to decimal.

$y = - 15$

Step 2

Find the point at $x = 0$ .

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

$f (0) = 15 {(0)}^{3} - 3 {(0)}^{2} + 0 + 4$

Simplify the result.

Remove parentheses.

$f (0) = 15 {(0)}^{3} - 3 {(0)}^{2} + 0 + 4$

Simplify each term.

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

$f (0) = 15 \cdot 0 - 3 {(0)}^{2} + 0 + 4$

Multiply $15$ by $0$ .

$f (0) = 0 - 3 {(0)}^{2} + 0 + 4$

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

$f (0) = 0 - 3 \cdot 0 + 0 + 4$

Multiply $- 3$ by $0$ .

$f (0) = 0 + 0 + 0 + 4$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 4$

Add $0$ and $0$ .

$f (0) = 0 + 4$

Add $0$ and $4$ .

$f (0) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 3

Find the point at $x = 1$ .

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

$f (1) = 15 {(1)}^{3} - 3 {(1)}^{2} + 1 + 4$

Simplify the result.

Remove parentheses.

$f (1) = 15 {(1)}^{3} - 3 {(1)}^{2} + 1 + 4$

Simplify each term.

One to any power is one.

$f (1) = 15 \cdot 1 - 3 {(1)}^{2} + 1 + 4$

Multiply $15$ by $1$ .

$f (1) = 15 - 3 {(1)}^{2} + 1 + 4$

One to any power is one.

$f (1) = 15 - 3 \cdot 1 + 1 + 4$

Multiply $- 3$ by $1$ .

$f (1) = 15 - 3 + 1 + 4$

Simplify by adding and subtracting.

Subtract $3$ from $15$ .

$f (1) = 12 + 1 + 4$

Add $12$ and $1$ .

$f (1) = 13 + 4$

Add $13$ and $4$ .

$f (1) = 17$

The final answer is $17$ .

$17$

Convert $17$ to decimal.

$y = 17$

Step 4

Find the point at $x = 2$ .

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

$f (2) = 15 {(2)}^{3} - 3 {(2)}^{2} + 2 + 4$

Simplify the result.

Remove parentheses.

$f (2) = 15 {(2)}^{3} - 3 {(2)}^{2} + 2 + 4$

Simplify each term.

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

$f (2) = 15 \cdot 8 - 3 {(2)}^{2} + 2 + 4$

Multiply $15$ by $8$ .

$f (2) = 120 - 3 {(2)}^{2} + 2 + 4$

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

$f (2) = 120 - 3 \cdot 4 + 2 + 4$

Multiply $- 3$ by $4$ .

$f (2) = 120 - 12 + 2 + 4$

Simplify by adding and subtracting.

Subtract $12$ from $120$ .

$f (2) = 108 + 2 + 4$

Add $108$ and $2$ .

$f (2) = 110 + 4$

Add $110$ and $4$ .

$f (2) = 114$

The final answer is $114$ .

$114$

Convert $114$ to decimal.

$y = 114$

Step 5

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = 15 {(3)}^{3} - 3 {(3)}^{2} + 3 + 4$

Simplify the result.

Remove parentheses.

$f (3) = 15 {(3)}^{3} - 3 {(3)}^{2} + 3 + 4$

Simplify each term.

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

$f (3) = 15 \cdot 27 - 3 {(3)}^{2} + 3 + 4$

Multiply $15$ by $27$ .

$f (3) = 405 - 3 {(3)}^{2} + 3 + 4$

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

$f (3) = 405 - 3 \cdot 9 + 3 + 4$

Multiply $- 3$ by $9$ .

$f (3) = 405 - 27 + 3 + 4$

Simplify by adding and subtracting.

Subtract $27$ from $405$ .

$f (3) = 378 + 3 + 4$

Add $378$ and $3$ .

$f (3) = 381 + 4$

Add $381$ and $4$ .

$f (3) = 385$

The final answer is $385$ .

$385$

Convert $385$ to decimal.

$y = 385$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & - 15 \\ 0 & 4 \\ 1 & 17 \\ 2 & 114 \\ 3 & 385 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & - 15 \\ 0 & 4 \\ 1 & 17 \\ 2 & 114 \\ 3 & 385 \end{array}$

Step 8

Graph P(x)=15x^3-3x^2+x+4

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