Pre-Algebra Examples

$y = 4 x^{2} \cdot (32 x) + 18$

Step 1

Find the point at $x = - 2$ .

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Step 1.1

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

$f (- 2) = 128 {(- 2)}^{3} + 18$

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

$f (- 2) = 128 \cdot - 8 + 18$

Step 1.2.1.2

Multiply $128$ by $- 8$ .

$f (- 2) = - 1024 + 18$

Step 1.2.2

Add $- 1024$ and $18$ .

$f (- 2) = - 1006$

Step 1.2.3

The final answer is $- 1006$ .

$- 1006$

Step 1.3

Convert $- 1006$ to decimal.

$y = - 1006$

Step 2

Find the point at $x = - 1$ .

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Step 2.1

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

$f (- 1) = 128 {(- 1)}^{3} + 18$

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

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

$f (- 1) = 128 \cdot - 1 + 18$

Step 2.2.1.2

Multiply $128$ by $- 1$ .

$f (- 1) = - 128 + 18$

Step 2.2.2

Add $- 128$ and $18$ .

$f (- 1) = - 110$

Step 2.2.3

The final answer is $- 110$ .

$- 110$

Step 2.3

Convert $- 110$ to decimal.

$y = - 110$

Step 3

Find the point at $x = 0$ .

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Step 3.1

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

$f (0) = 128 {(0)}^{3} + 18$

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

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

$f (0) = 128 \cdot 0 + 18$

Step 3.2.1.2

Multiply $128$ by $0$ .

$f (0) = 0 + 18$

Step 3.2.2

Add $0$ and $18$ .

$f (0) = 18$

Step 3.2.3

The final answer is $18$ .

$18$

Step 3.3

Convert $18$ to decimal.

$y = 18$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

$f (1) = 128 {(1)}^{3} + 18$

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

One to any power is one.

$f (1) = 128 \cdot 1 + 18$

Step 4.2.1.2

Multiply $128$ by $1$ .

$f (1) = 128 + 18$

Step 4.2.2

Add $128$ and $18$ .

$f (1) = 146$

Step 4.2.3

The final answer is $146$ .

$146$

Step 4.3

Convert $146$ to decimal.

$y = 146$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

$f (2) = 128 {(2)}^{3} + 18$

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 $2$ to the power of $3$ .

$f (2) = 128 \cdot 8 + 18$

Step 5.2.1.2

Multiply $128$ by $8$ .

$f (2) = 1024 + 18$

Step 5.2.2

Add $1024$ and $18$ .

$f (2) = 1042$

Step 5.2.3

The final answer is $1042$ .

$1042$

Step 5.3

Convert $1042$ to decimal.

$y = 1042$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 1006 \\ - 1 & - 110 \\ 0 & 18 \\ 1 & 146 \\ 2 & 1042 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 1006 \\ - 1 & - 110 \\ 0 & 18 \\ 1 & 146 \\ 2 & 1042 \end{array}$

Step 8