Pre-Algebra Examples

$10 a^{3} + 9 a - 1 - 6 a^{2}$

Step 1

Find the point at $x = - 1$ .

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Step 1.1

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

$f (- 1) = 10 {(- 1)}^{3} + 9 (- 1) - 1 - 6 {(- 1)}^{2}$

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

$f (- 1) = 10 \cdot - 1 + 9 (- 1) - 1 - 6 {(- 1)}^{2}$

Step 1.2.1.2

Multiply $10$ by $- 1$ .

$f (- 1) = - 10 + 9 (- 1) - 1 - 6 {(- 1)}^{2}$

Step 1.2.1.3

Multiply $9$ by $- 1$ .

$f (- 1) = - 10 - 9 - 1 - 6 {(- 1)}^{2}$

Step 1.2.1.4

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

$f (- 1) = - 10 - 9 - 1 - 6 \cdot 1$

Step 1.2.1.5

Multiply $- 6$ by $1$ .

$f (- 1) = - 10 - 9 - 1 - 6$

Step 1.2.2

Simplify by subtracting numbers.

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Step 1.2.2.1

Subtract $9$ from $- 10$ .

$f (- 1) = - 19 - 1 - 6$

Step 1.2.2.2

Subtract $1$ from $- 19$ .

$f (- 1) = - 20 - 6$

Step 1.2.2.3

Subtract $6$ from $- 20$ .

$f (- 1) = - 26$

Step 1.2.3

The final answer is $- 26$ .

$- 26$

Step 1.3

Convert $- 26$ to decimal.

$y = - 26$

Step 2

Find the point at $x = 0$ .

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Step 2.1

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

$f (0) = 10 {(0)}^{3} + 9 (0) - 1 - 6 {(0)}^{2}$

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

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

$f (0) = 10 \cdot 0 + 9 (0) - 1 - 6 {(0)}^{2}$

Step 2.2.1.2

Multiply $10$ by $0$ .

$f (0) = 0 + 9 (0) - 1 - 6 {(0)}^{2}$

Step 2.2.1.3

Multiply $9$ by $0$ .

$f (0) = 0 + 0 - 1 - 6 {(0)}^{2}$

Step 2.2.1.4

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

$f (0) = 0 + 0 - 1 - 6 \cdot 0$

Step 2.2.1.5

Multiply $- 6$ by $0$ .

$f (0) = 0 + 0 - 1 + 0$

Step 2.2.2

Simplify by adding and subtracting.

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Step 2.2.2.1

Add $0$ and $0$ .

$f (0) = 0 - 1 + 0$

Step 2.2.2.2

Subtract $1$ from $0$ .

$f (0) = - 1 + 0$

Step 2.2.2.3

Add $- 1$ and $0$ .

$f (0) = - 1$

Step 2.2.3

The final answer is $- 1$ .

$- 1$

Step 2.3

Convert $- 1$ to decimal.

$y = - 1$

Step 3

Find the point at $x = 1$ .

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Step 3.1

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

$f (1) = 10 {(1)}^{3} + 9 (1) - 1 - 6 {(1)}^{2}$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

One to any power is one.

$f (1) = 10 \cdot 1 + 9 (1) - 1 - 6 {(1)}^{2}$

Step 3.2.1.2

Multiply $10$ by $1$ .

$f (1) = 10 + 9 (1) - 1 - 6 {(1)}^{2}$

Step 3.2.1.3

Multiply $9$ by $1$ .

$f (1) = 10 + 9 - 1 - 6 {(1)}^{2}$

Step 3.2.1.4

One to any power is one.

$f (1) = 10 + 9 - 1 - 6 \cdot 1$

Step 3.2.1.5

Multiply $- 6$ by $1$ .

$f (1) = 10 + 9 - 1 - 6$

Step 3.2.2

Simplify by adding and subtracting.

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Step 3.2.2.1

Add $10$ and $9$ .

$f (1) = 19 - 1 - 6$

Step 3.2.2.2

Subtract $1$ from $19$ .

$f (1) = 18 - 6$

Step 3.2.2.3

Subtract $6$ from $18$ .

$f (1) = 12$

Step 3.2.3

The final answer is $12$ .

$12$

Step 3.3

Convert $12$ to decimal.

$y = 12$

Step 4

Find the point at $x = 2$ .

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Step 4.1

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

$f (2) = 10 {(2)}^{3} + 9 (2) - 1 - 6 {(2)}^{2}$

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

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

$f (2) = 10 \cdot 8 + 9 (2) - 1 - 6 {(2)}^{2}$

Step 4.2.1.2

Multiply $10$ by $8$ .

$f (2) = 80 + 9 (2) - 1 - 6 {(2)}^{2}$

Step 4.2.1.3

Multiply $9$ by $2$ .

$f (2) = 80 + 18 - 1 - 6 {(2)}^{2}$

Step 4.2.1.4

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

$f (2) = 80 + 18 - 1 - 6 \cdot 4$

Step 4.2.1.5

Multiply $- 6$ by $4$ .

$f (2) = 80 + 18 - 1 - 24$

Step 4.2.2

Simplify by adding and subtracting.

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Step 4.2.2.1

Add $80$ and $18$ .

$f (2) = 98 - 1 - 24$

Step 4.2.2.2

Subtract $1$ from $98$ .

$f (2) = 97 - 24$

Step 4.2.2.3

Subtract $24$ from $97$ .

$f (2) = 73$

Step 4.2.3

The final answer is $73$ .

$73$

Step 4.3

Convert $73$ to decimal.

$y = 73$

Step 5

Find the point at $x = 3$ .

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Step 5.1

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

$f (3) = 10 {(3)}^{3} + 9 (3) - 1 - 6 {(3)}^{2}$

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

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

$f (3) = 10 \cdot 27 + 9 (3) - 1 - 6 {(3)}^{2}$

Step 5.2.1.2

Multiply $10$ by $27$ .

$f (3) = 270 + 9 (3) - 1 - 6 {(3)}^{2}$

Step 5.2.1.3

Multiply $9$ by $3$ .

$f (3) = 270 + 27 - 1 - 6 {(3)}^{2}$

Step 5.2.1.4

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

$f (3) = 270 + 27 - 1 - 6 \cdot 9$

Step 5.2.1.5

Multiply $- 6$ by $9$ .

$f (3) = 270 + 27 - 1 - 54$

Step 5.2.2

Simplify by adding and subtracting.

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Step 5.2.2.1

Add $270$ and $27$ .

$f (3) = 297 - 1 - 54$

Step 5.2.2.2

Subtract $1$ from $297$ .

$f (3) = 296 - 54$

Step 5.2.2.3

Subtract $54$ from $296$ .

$f (3) = 242$

Step 5.2.3

The final answer is $242$ .

$242$

Step 5.3

Convert $242$ to decimal.

$y = 242$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & - 26 \\ 0 & - 1 \\ 1 & 12 \\ 2 & 73 \\ 3 & 242 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & - 26 \\ 0 & - 1 \\ 1 & 12 \\ 2 & 73 \\ 3 & 242 \end{array}$

Step 8