Graph f(x)=-(x-1)(x^2-9)

$f (x) = - (x - 1) (x^{2} - 9)$

Find the point at $x = - 1$ .

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

$f (- 1) = - {(- 1)}^{3} + 9 (- 1) + {(- 1)}^{2} - 9$

Simplify the result.

Simplify each term.

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{3}$ .

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

$f (- 1) = (- 1) {(- 1)}^{3} + 9 (- 1) + {(- 1)}^{2} - 9$

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

$f (- 1) = {(- 1)}^{1 + 3} + 9 (- 1) + {(- 1)}^{2} - 9$

Add $1$ and $3$ .

$f (- 1) = {(- 1)}^{4} + 9 (- 1) + {(- 1)}^{2} - 9$

Raise $- 1$ to the power of $4$ .

$f (- 1) = 1 + 9 (- 1) + {(- 1)}^{2} - 9$

Multiply $9$ by $- 1$ .

$f (- 1) = 1 - 9 + {(- 1)}^{2} - 9$

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

$f (- 1) = 1 - 9 + 1 - 9$

Simplify by adding and subtracting.

Subtract $9$ from $1$ .

$f (- 1) = - 8 + 1 - 9$

Add $- 8$ and $1$ .

$f (- 1) = - 7 - 9$

Subtract $9$ from $- 7$ .

$f (- 1) = - 16$

The final answer is $- 16$ .

$- 16$

Convert $- 16$ to decimal.

$y = - 16$

Find the point at $x = 0$ .

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

$f (0) = - {(0)}^{3} + 9 (0) + {(0)}^{2} - 9$

Simplify the result.

Simplify each term.

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

$f (0) = - 0 + 9 (0) + {(0)}^{2} - 9$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 9 (0) + {(0)}^{2} - 9$

Multiply $9$ by $0$ .

$f (0) = 0 + 0 + {(0)}^{2} - 9$

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

$f (0) = 0 + 0 + 0 - 9$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 + 0 - 9$

Add $0$ and $0$ .

$f (0) = 0 - 9$

Subtract $9$ from $0$ .

$f (0) = - 9$

The final answer is $- 9$ .

$- 9$

Convert $- 9$ to decimal.

$y = - 9$

Find the point at $x = 1$ .

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

$f (1) = - {(1)}^{3} + 9 (1) + {(1)}^{2} - 9$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 1 \cdot 1 + 9 (1) + {(1)}^{2} - 9$

Multiply $- 1$ by $1$ .

$f (1) = - 1 + 9 (1) + {(1)}^{2} - 9$

Multiply $9$ by $1$ .

$f (1) = - 1 + 9 + {(1)}^{2} - 9$

One to any power is one.

$f (1) = - 1 + 9 + 1 - 9$

Simplify by adding and subtracting.

Add $- 1$ and $9$ .

$f (1) = 8 + 1 - 9$

Add $8$ and $1$ .

$f (1) = 9 - 9$

Subtract $9$ from $9$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 2$ .

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

$f (2) = - {(2)}^{3} + 9 (2) + {(2)}^{2} - 9$

Simplify the result.

Simplify each term.

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

$f (2) = - 1 \cdot 8 + 9 (2) + {(2)}^{2} - 9$

Multiply $- 1$ by $8$ .

$f (2) = - 8 + 9 (2) + {(2)}^{2} - 9$

Multiply $9$ by $2$ .

$f (2) = - 8 + 18 + {(2)}^{2} - 9$

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

$f (2) = - 8 + 18 + 4 - 9$

Simplify by adding and subtracting.

Add $- 8$ and $18$ .

$f (2) = 10 + 4 - 9$

Add $10$ and $4$ .

$f (2) = 14 - 9$

Subtract $9$ from $14$ .

$f (2) = 5$

The final answer is $5$ .

$5$

Convert $5$ to decimal.

$y = 5$

Find the point at $x = 3$ .

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

$f (3) = - {(3)}^{3} + 9 (3) + {(3)}^{2} - 9$

Simplify the result.

Simplify each term.

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

$f (3) = - 1 \cdot 27 + 9 (3) + {(3)}^{2} - 9$

Multiply $- 1$ by $27$ .

$f (3) = - 27 + 9 (3) + {(3)}^{2} - 9$

Multiply $9$ by $3$ .

$f (3) = - 27 + 27 + {(3)}^{2} - 9$

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

$f (3) = - 27 + 27 + 9 - 9$

Simplify by adding and subtracting.

Add $- 27$ and $27$ .

$f (3) = 0 + 9 - 9$

Add $0$ and $9$ .

$f (3) = 9 - 9$

Subtract $9$ from $9$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

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

$\begin{array}{c} x & y \\ - 1 & - 16 \\ 0 & - 9 \\ 1 & 0 \\ 2 & 5 \\ 3 & 0 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 1 & - 16 \\ 0 & - 9 \\ 1 & 0 \\ 2 & 5 \\ 3 & 0 \end{array}$

Graph f(x)=-(x-1)(x^2-9)

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