Graph y=-7x^3+8x^2+x

$y = - 7 x^{3} + 8 x^{2} + x$

Step 1

Find the point at $x = - 1$ .

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

$f (- 1) = - 7 {(- 1)}^{3} + 8 {(- 1)}^{2} - 1$

Simplify the result.

Remove parentheses.

$f (- 1) = - 7 {(- 1)}^{3} + 8 {(- 1)}^{2} - 1$

Simplify each term.

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

$f (- 1) = - 7 \cdot - 1 + 8 {(- 1)}^{2} - 1$

Multiply $- 7$ by $- 1$ .

$f (- 1) = 7 + 8 {(- 1)}^{2} - 1$

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

$f (- 1) = 7 + 8 \cdot 1 - 1$

Multiply $8$ by $1$ .

$f (- 1) = 7 + 8 - 1$

Simplify by adding and subtracting.

Add $7$ and $8$ .

$f (- 1) = 15 - 1$

Subtract $1$ from $15$ .

$f (- 1) = 14$

The final answer is $14$ .

$14$

Convert $14$ to decimal.

$y = 14$

Step 2

Find the point at $x = 0$ .

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

$f (0) = - 7 {(0)}^{3} + 8 {(0)}^{2} + 0$

Simplify the result.

Remove parentheses.

$f (0) = - 7 {(0)}^{3} + 8 {(0)}^{2} + 0$

Simplify each term.

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

$f (0) = - 7 \cdot 0 + 8 {(0)}^{2} + 0$

Multiply $- 7$ by $0$ .

$f (0) = 0 + 8 {(0)}^{2} + 0$

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

$f (0) = 0 + 8 \cdot 0 + 0$

Multiply $8$ by $0$ .

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

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0$

Add $0$ and $0$ .

$f (0) = 0$

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.

$f (1) = - 7 {(1)}^{3} + 8 {(1)}^{2} + 1$

Simplify the result.

Remove parentheses.

$f (1) = - 7 {(1)}^{3} + 8 {(1)}^{2} + 1$

Simplify each term.

One to any power is one.

$f (1) = - 7 \cdot 1 + 8 {(1)}^{2} + 1$

Multiply $- 7$ by $1$ .

$f (1) = - 7 + 8 {(1)}^{2} + 1$

One to any power is one.

$f (1) = - 7 + 8 \cdot 1 + 1$

Multiply $8$ by $1$ .

$f (1) = - 7 + 8 + 1$

Simplify by adding numbers.

Add $- 7$ and $8$ .

$f (1) = 1 + 1$

Add $1$ and $1$ .

$f (1) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 4

Find the point at $x = 2$ .

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

$f (2) = - 7 {(2)}^{3} + 8 {(2)}^{2} + 2$

Simplify the result.

Remove parentheses.

$f (2) = - 7 {(2)}^{3} + 8 {(2)}^{2} + 2$

Simplify each term.

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

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

Multiply $- 7$ by $8$ .

$f (2) = - 56 + 8 {(2)}^{2} + 2$

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

$f (2) = - 56 + 8 \cdot 4 + 2$

Multiply $8$ by $4$ .

$f (2) = - 56 + 32 + 2$

Simplify by adding numbers.

Add $- 56$ and $32$ .

$f (2) = - 24 + 2$

Add $- 24$ and $2$ .

$f (2) = - 22$

The final answer is $- 22$ .

$- 22$

Convert $- 22$ to decimal.

$y = - 22$

Step 5

Find the point at $x = 3$ .

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

$f (3) = - 7 {(3)}^{3} + 8 {(3)}^{2} + 3$

Simplify the result.

Remove parentheses.

$f (3) = - 7 {(3)}^{3} + 8 {(3)}^{2} + 3$

Simplify each term.

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

$f (3) = - 7 \cdot 27 + 8 {(3)}^{2} + 3$

Multiply $- 7$ by $27$ .

$f (3) = - 189 + 8 {(3)}^{2} + 3$

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

$f (3) = - 189 + 8 \cdot 9 + 3$

Multiply $8$ by $9$ .

$f (3) = - 189 + 72 + 3$

Simplify by adding numbers.

Add $- 189$ and $72$ .

$f (3) = - 117 + 3$

Add $- 117$ and $3$ .

$f (3) = - 114$

The final answer is $- 114$ .

$- 114$

Convert $- 114$ to decimal.

$y = - 114$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & 14 \\ 0 & 0 \\ 1 & 2 \\ 2 & - 22 \\ 3 & - 114 \end{array}$

Step 7

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 1 & 14 \\ 0 & 0 \\ 1 & 2 \\ 2 & - 22 \\ 3 & - 114 \end{array}$

Step 8

Graph y=-7x^3+8x^2+x

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