Trigonometry Examples

$a = (- t^{3} + 3.4 t^{2} + 1.8 t)$

Step 1

Find the point at $x = 0$ .

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Step 1.1

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

$f (0) = - {(0)}^{3} + 3.4 {(0)}^{2} + 1.8 (0)$

Step 1.2

Simplify the result.

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Step 1.2.1

Remove parentheses.

$f (0) = - {(0)}^{3} + 3.4 {(0)}^{2} + 1.8 (0)$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

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

$f (0) = - 0 + 3.4 {(0)}^{2} + 1.8 (0)$

Step 1.2.2.2

Multiply $- 1$ by $0$ .

$f (0) = 0 + 3.4 {(0)}^{2} + 1.8 (0)$

Step 1.2.2.3

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

$f (0) = 0 + 3.4 \cdot 0 + 1.8 (0)$

Step 1.2.2.4

Multiply $3.4$ by $0$ .

$f (0) = 0 + 0 + 1.8 (0)$

Step 1.2.2.5

Multiply $1.8$ by $0$ .

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

Step 1.2.3

Simplify by adding numbers.

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Step 1.2.3.1

Add $0$ and $0$ .

$f (0) = 0 + 0$

Step 1.2.3.2

Add $0$ and $0$ .

$f (0) = 0$

Step 1.2.4

The final answer is $0$ .

$0$

Step 1.3

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = 1$ .

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Step 2.1

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

$f (1) = - {(1)}^{3} + 3.4 {(1)}^{2} + 1.8 (1)$

Step 2.2

Simplify the result.

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Step 2.2.1

Remove parentheses.

$f (1) = - {(1)}^{3} + 3.4 {(1)}^{2} + 1.8 (1)$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

One to any power is one.

$f (1) = - 1 \cdot 1 + 3.4 {(1)}^{2} + 1.8 (1)$

Step 2.2.2.2

Multiply $- 1$ by $1$ .

$f (1) = - 1 + 3.4 {(1)}^{2} + 1.8 (1)$

Step 2.2.2.3

One to any power is one.

$f (1) = - 1 + 3.4 \cdot 1 + 1.8 (1)$

Step 2.2.2.4

Multiply $3.4$ by $1$ .

$f (1) = - 1 + 3.4 + 1.8 (1)$

Step 2.2.2.5

Multiply $1.8$ by $1$ .

$f (1) = - 1 + 3.4 + 1.8$

Step 2.2.3

Simplify by adding numbers.

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Step 2.2.3.1

Add $- 1$ and $3.4$ .

$f (1) = 2.4 + 1.8$

Step 2.2.3.2

Add $2.4$ and $1.8$ .

$f (1) = 4.2$

Step 2.2.4

The final answer is $4.2$ .

$4.2$

Step 3

Find the point at $x = 2$ .

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Step 3.1

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

$f (2) = - {(2)}^{3} + 3.4 {(2)}^{2} + 1.8 (2)$

Step 3.2

Simplify the result.

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Step 3.2.1

Remove parentheses.

$f (2) = - {(2)}^{3} + 3.4 {(2)}^{2} + 1.8 (2)$

Step 3.2.2

Simplify each term.

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Step 3.2.2.1

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

$f (2) = - 1 \cdot 8 + 3.4 {(2)}^{2} + 1.8 (2)$

Step 3.2.2.2

Multiply $- 1$ by $8$ .

$f (2) = - 8 + 3.4 {(2)}^{2} + 1.8 (2)$

Step 3.2.2.3

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

$f (2) = - 8 + 3.4 \cdot 4 + 1.8 (2)$

Step 3.2.2.4

Multiply $3.4$ by $4$ .

$f (2) = - 8 + 13.6 + 1.8 (2)$

Step 3.2.2.5

Multiply $1.8$ by $2$ .

$f (2) = - 8 + 13.6 + 3.6$

Step 3.2.3

Simplify by adding numbers.

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Step 3.2.3.1

Add $- 8$ and $13.6$ .

$f (2) = 5.6 + 3.6$

Step 3.2.3.2

Add $5.6$ and $3.6$ .

$f (2) = 9.2$

Step 3.2.4

The final answer is $9.2$ .

$9.2$

Step 4

Find the point at $x = 3$ .

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Step 4.1

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

$f (3) = - {(3)}^{3} + 3.4 {(3)}^{2} + 1.8 (3)$

Step 4.2

Simplify the result.

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Step 4.2.1

Remove parentheses.

$f (3) = - {(3)}^{3} + 3.4 {(3)}^{2} + 1.8 (3)$

Step 4.2.2

Simplify each term.

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Step 4.2.2.1

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

$f (3) = - 1 \cdot 27 + 3.4 {(3)}^{2} + 1.8 (3)$

Step 4.2.2.2

Multiply $- 1$ by $27$ .

$f (3) = - 27 + 3.4 {(3)}^{2} + 1.8 (3)$

Step 4.2.2.3

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

$f (3) = - 27 + 3.4 \cdot 9 + 1.8 (3)$

Step 4.2.2.4

Multiply $3.4$ by $9$ .

$f (3) = - 27 + 30.6 + 1.8 (3)$

Step 4.2.2.5

Multiply $1.8$ by $3$ .

$f (3) = - 27 + 30.6 + 5.4$

Step 4.2.3

Simplify by adding numbers.

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Step 4.2.3.1

Add $- 27$ and $30.6$ .

$f (3) = 3.6 + 5.4$

Step 4.2.3.2

Add $3.6$ and $5.4$ .

$f (3) = 9$

Step 4.2.4

The final answer is $9$ .

$9$

Step 5

Find the point at $x = 4$ .

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Step 5.1

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

$f (4) = - {(4)}^{3} + 3.4 {(4)}^{2} + 1.8 (4)$

Step 5.2

Simplify the result.

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Step 5.2.1

Remove parentheses.

$f (4) = - {(4)}^{3} + 3.4 {(4)}^{2} + 1.8 (4)$

Step 5.2.2

Simplify each term.

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Step 5.2.2.1

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

$f (4) = - 1 \cdot 64 + 3.4 {(4)}^{2} + 1.8 (4)$

Step 5.2.2.2

Multiply $- 1$ by $64$ .

$f (4) = - 64 + 3.4 {(4)}^{2} + 1.8 (4)$

Step 5.2.2.3

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

$f (4) = - 64 + 3.4 \cdot 16 + 1.8 (4)$

Step 5.2.2.4

Multiply $3.4$ by $16$ .

$f (4) = - 64 + 54.4 + 1.8 (4)$

Step 5.2.2.5

Multiply $1.8$ by $4$ .

$f (4) = - 64 + 54.4 + 7.2$

Step 5.2.3

Simplify by adding numbers.

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Step 5.2.3.1

Add $- 64$ and $54.4$ .

$f (4) = - 9.6 + 7.2$

Step 5.2.3.2

Add $- 9.6$ and $7.2$ .

$f (4) = - 2.4$

Step 5.2.4

The final answer is $- 2.4$ .

$- 2.4$

Step 6

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 4.2 \\ 2 & 9.2 \\ 3 & 9 \\ 4 & - 2.4 \end{array}$

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 4.2 \\ 2 & 9.2 \\ 3 & 9 \\ 4 & - 2.4 \end{array}$

Step 8