Graph h(x)=1/8x^3-x^2

$h (x) = \frac{1}{8} x^{3} - x^{2}$

Step 1

Find the point at $x = 2$ .

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

$f (2) = \frac{{(2)}^{3}}{8} - {(2)}^{2}$

Simplify the result.

Simplify each term.

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

$f (2) = \frac{8}{8} - {(2)}^{2}$

Divide $8$ by $8$ .

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

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

$f (2) = 1 - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$f (2) = 1 - 4$

Subtract $4$ from $1$ .

$f (2) = - 3$

The final answer is $- 3$ .

$- 3$

Convert $- 3$ to decimal.

$y = - 3$

Step 2

Find the point at $x = 4$ .

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

$f (4) = \frac{{(4)}^{3}}{8} - {(4)}^{2}$

Simplify the result.

Simplify each term.

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

$f (4) = \frac{64}{8} - {(4)}^{2}$

Divide $64$ by $8$ .

$f (4) = 8 - {(4)}^{2}$

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

$f (4) = 8 - 1 \cdot 16$

Multiply $- 1$ by $16$ .

$f (4) = 8 - 16$

Subtract $16$ from $8$ .

$f (4) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Step 3

Find the point at $x = 6$ .

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

$f (6) = \frac{{(6)}^{3}}{8} - {(6)}^{2}$

Simplify the result.

Simplify each term.

Raise $6$ to the power of $3$ .

$f (6) = \frac{216}{8} - {(6)}^{2}$

Divide $216$ by $8$ .

$f (6) = 27 - {(6)}^{2}$

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

$f (6) = 27 - 1 \cdot 36$

Multiply $- 1$ by $36$ .

$f (6) = 27 - 36$

Subtract $36$ from $27$ .

$f (6) = - 9$

The final answer is $- 9$ .

$- 9$

Convert $- 9$ to decimal.

$y = - 9$

Step 4

Find the point at $x = 1$ .

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

$f (1) = \frac{{(1)}^{3}}{8} - {(1)}^{2}$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = \frac{1}{8} - {(1)}^{2}$

One to any power is one.

$f (1) = \frac{1}{8} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$f (1) = \frac{1}{8} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$f (1) = \frac{1}{8} - 1 \cdot \frac{8}{8}$

Combine $- 1$ and $\frac{8}{8}$ .

$f (1) = \frac{1}{8} + \frac{- 1 \cdot 8}{8}$

Combine the numerators over the common denominator.

$f (1) = \frac{1 - 1 \cdot 8}{8}$

Simplify the numerator.

Multiply $- 1$ by $8$ .

$f (1) = \frac{1 - 8}{8}$

Subtract $8$ from $1$ .

$f (1) = \frac{- 7}{8}$

Move the negative in front of the fraction.

$f (1) = - \frac{7}{8}$

The final answer is $- \frac{7}{8}$ .

$- \frac{7}{8}$

Convert $- \frac{7}{8}$ to decimal.

$y = - 0.875$

Step 5

Find the point at $x = 3$ .

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

$f (3) = \frac{{(3)}^{3}}{8} - {(3)}^{2}$

Simplify the result.

Simplify each term.

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

$f (3) = \frac{27}{8} - {(3)}^{2}$

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

$f (3) = \frac{27}{8} - 1 \cdot 9$

Multiply $- 1$ by $9$ .

$f (3) = \frac{27}{8} - 9$

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$f (3) = \frac{27}{8} - 9 \cdot \frac{8}{8}$

Combine $- 9$ and $\frac{8}{8}$ .

$f (3) = \frac{27}{8} + \frac{- 9 \cdot 8}{8}$

Combine the numerators over the common denominator.

$f (3) = \frac{27 - 9 \cdot 8}{8}$

Simplify the numerator.

Multiply $- 9$ by $8$ .

$f (3) = \frac{27 - 72}{8}$

Subtract $72$ from $27$ .

$f (3) = \frac{- 45}{8}$

Move the negative in front of the fraction.

$f (3) = - \frac{45}{8}$

The final answer is $- \frac{45}{8}$ .

$- \frac{45}{8}$

Convert $- \frac{45}{8}$ to decimal.

$y = - 5.625$

Step 6

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

$\begin{array}{c} x & y \\ 1 & - 0.875 \\ 2 & - 3 \\ 3 & - 5.625 \\ 4 & - 8 \\ 6 & - 9 \end{array}$

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

$\begin{array}{c} x & y \\ 1 & - 0.875 \\ 2 & - 3 \\ 3 & - 5.625 \\ 4 & - 8 \\ 6 & - 9 \end{array}$

Step 8

Graph h(x)=1/8x^3-x^2

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