Pre-Algebra Examples

$t (d) = - 0.1 d^{3} + 1.2 d^{2} - 4.4 d + 14.8$

Step 1

Find the point at $x = 2$ .

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Step 1.1

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

$f (2) = - 0.1 {(2)}^{3} + 1.2 {(2)}^{2} - 4.4 \cdot 2 + 14.8$

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 $3$ .

$f (2) = - 0.1 \cdot 8 + 1.2 {(2)}^{2} - 4.4 \cdot 2 + 14.8$

Step 1.2.1.2

Multiply $- 0.1$ by $8$ .

$f (2) = - 0.8 + 1.2 {(2)}^{2} - 4.4 \cdot 2 + 14.8$

Step 1.2.1.3

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

$f (2) = - 0.8 + 1.2 \cdot 4 - 4.4 \cdot 2 + 14.8$

Step 1.2.1.4

Multiply $1.2$ by $4$ .

$f (2) = - 0.8 + 4.8 - 4.4 \cdot 2 + 14.8$

Step 1.2.1.5

Multiply $- 4.4$ by $2$ .

$f (2) = - 0.8 + 4.8 - 8.8 + 14.8$

Step 1.2.2

Simplify by adding and subtracting.

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Step 1.2.2.1

Add $- 0.8$ and $4.8$ .

$f (2) = 4 - 8.8 + 14.8$

Step 1.2.2.2

Subtract $8.8$ from $4$ .

$f (2) = - 4.8 + 14.8$

Step 1.2.2.3

Add $- 4.8$ and $14.8$ .

$f (2) = 10$

Step 1.2.3

The final answer is $10$ .

$10$

Step 2

Find the point at $x = 3$ .

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Step 2.1

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

$f (3) = - 0.1 {(3)}^{3} + 1.2 {(3)}^{2} - 4.4 \cdot 3 + 14.8$

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 $3$ to the power of $3$ .

$f (3) = - 0.1 \cdot 27 + 1.2 {(3)}^{2} - 4.4 \cdot 3 + 14.8$

Step 2.2.1.2

Multiply $- 0.1$ by $27$ .

$f (3) = - 2.7 + 1.2 {(3)}^{2} - 4.4 \cdot 3 + 14.8$

Step 2.2.1.3

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

$f (3) = - 2.7 + 1.2 \cdot 9 - 4.4 \cdot 3 + 14.8$

Step 2.2.1.4

Multiply $1.2$ by $9$ .

$f (3) = - 2.7 + 10.8 - 4.4 \cdot 3 + 14.8$

Step 2.2.1.5

Multiply $- 4.4$ by $3$ .

$f (3) = - 2.7 + 10.8 - 13.2 + 14.8$

Step 2.2.2

Simplify by adding and subtracting.

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Step 2.2.2.1

Add $- 2.7$ and $10.8$ .

$f (3) = 8.1 - 13.2 + 14.8$

Step 2.2.2.2

Subtract $13.2$ from $8.1$ .

$f (3) = - 5.1 + 14.8$

Step 2.2.2.3

Add $- 5.1$ and $14.8$ .

$f (3) = 9.7$

Step 2.2.3

The final answer is $9.7$ .

$9.7$

Step 3

Find the point at $x = 4$ .

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Step 3.1

Replace the variable $x$ with $4$ in the expression.

$f (4) = - 0.1 {(4)}^{3} + 1.2 {(4)}^{2} - 4.4 \cdot 4 + 14.8$

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

Raise $4$ to the power of $3$ .

$f (4) = - 0.1 \cdot 64 + 1.2 {(4)}^{2} - 4.4 \cdot 4 + 14.8$

Step 3.2.1.2

Multiply $- 0.1$ by $64$ .

$f (4) = - 6.4 + 1.2 {(4)}^{2} - 4.4 \cdot 4 + 14.8$

Step 3.2.1.3

Raise $4$ to the power of $2$ .

$f (4) = - 6.4 + 1.2 \cdot 16 - 4.4 \cdot 4 + 14.8$

Step 3.2.1.4

Multiply $1.2$ by $16$ .

$f (4) = - 6.4 + 19.2 - 4.4 \cdot 4 + 14.8$

Step 3.2.1.5

Multiply $- 4.4$ by $4$ .

$f (4) = - 6.4 + 19.2 - 17.6 + 14.8$

Step 3.2.2

Simplify by adding and subtracting.

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Step 3.2.2.1

Add $- 6.4$ and $19.2$ .

$f (4) = 12.8 - 17.6 + 14.8$

Step 3.2.2.2

Subtract $17.6$ from $12.8$ .

$f (4) = - 4.8 + 14.8$

Step 3.2.2.3

Add $- 4.8$ and $14.8$ .

$f (4) = 10$

Step 3.2.3

The final answer is $10$ .

$10$

Step 4

Find the point at $x = 5$ .

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Step 4.1

Replace the variable $x$ with $5$ in the expression.

$f (5) = - 0.1 {(5)}^{3} + 1.2 {(5)}^{2} - 4.4 \cdot 5 + 14.8$

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 $5$ to the power of $3$ .

$f (5) = - 0.1 \cdot 125 + 1.2 {(5)}^{2} - 4.4 \cdot 5 + 14.8$

Step 4.2.1.2

Multiply $- 0.1$ by $125$ .

$f (5) = - 12.5 + 1.2 {(5)}^{2} - 4.4 \cdot 5 + 14.8$

Step 4.2.1.3

Raise $5$ to the power of $2$ .

$f (5) = - 12.5 + 1.2 \cdot 25 - 4.4 \cdot 5 + 14.8$

Step 4.2.1.4

Multiply $1.2$ by $25$ .

$f (5) = - 12.5 + 30 - 4.4 \cdot 5 + 14.8$

Step 4.2.1.5

Multiply $- 4.4$ by $5$ .

$f (5) = - 12.5 + 30 - 22 + 14.8$

Step 4.2.2

Simplify by adding and subtracting.

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Step 4.2.2.1

Add $- 12.5$ and $30$ .

$f (5) = 17.5 - 22 + 14.8$

Step 4.2.2.2

Subtract $22$ from $17.5$ .

$f (5) = - 4.5 + 14.8$

Step 4.2.2.3

Add $- 4.5$ and $14.8$ .

$f (5) = 10.3$

Step 4.2.3

The final answer is $10.3$ .

$10.3$

Step 5

Find the point at $x = 6$ .

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Step 5.1

Replace the variable $x$ with $6$ in the expression.

$f (6) = - 0.1 {(6)}^{3} + 1.2 {(6)}^{2} - 4.4 \cdot 6 + 14.8$

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 $6$ to the power of $3$ .

$f (6) = - 0.1 \cdot 216 + 1.2 {(6)}^{2} - 4.4 \cdot 6 + 14.8$

Step 5.2.1.2

Multiply $- 0.1$ by $216$ .

$f (6) = - 21.6 + 1.2 {(6)}^{2} - 4.4 \cdot 6 + 14.8$

Step 5.2.1.3

Raise $6$ to the power of $2$ .

$f (6) = - 21.6 + 1.2 \cdot 36 - 4.4 \cdot 6 + 14.8$

Step 5.2.1.4

Multiply $1.2$ by $36$ .

$f (6) = - 21.6 + 43.2 - 4.4 \cdot 6 + 14.8$

Step 5.2.1.5

Multiply $- 4.4$ by $6$ .

$f (6) = - 21.6 + 43.2 - 26.4 + 14.8$

Step 5.2.2

Simplify by adding and subtracting.

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Step 5.2.2.1

Add $- 21.6$ and $43.2$ .

$f (6) = 21.6 - 26.4 + 14.8$

Step 5.2.2.2

Subtract $26.4$ from $21.6$ .

$f (6) = - 4.8 + 14.8$

Step 5.2.2.3

Add $- 4.8$ and $14.8$ .

$f (6) = 10$

Step 5.2.3

The final answer is $10$ .

$10$

Step 6

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

$\begin{array}{c} x & y \\ 2 & 10 \\ 3 & 9.7 \\ 4 & 10 \\ 5 & 10.3 \\ 6 & 10 \end{array}$

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

$\begin{array}{c} x & y \\ 2 & 10 \\ 3 & 9.7 \\ 4 & 10 \\ 5 & 10.3 \\ 6 & 10 \end{array}$

Step 8