Graph f(x)=5x(2x-5)^2

$f (x) = 5 x {(2 x - 5)}^{2}$

Step 1

Find the point at $x = 0$ .

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

$f (0) = 5 (0) {(2 (0) - 5)}^{2}$

Simplify the result.

Multiply $5$ by $0$ .

$f (0) = 0 {(2 (0) - 5)}^{2}$

Multiply $2$ by $0$ .

$f (0) = 0 {(0 - 5)}^{2}$

Subtract $5$ from $0$ .

$f (0) = 0 {(- 5)}^{2}$

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

$f (0) = 0 \cdot 25$

Multiply $0$ by $25$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = 1$ .

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

$f (1) = 5 (1) {(2 (1) - 5)}^{2}$

Simplify the result.

Multiply $5$ by $1$ .

$f (1) = 5 {(2 (1) - 5)}^{2}$

Multiply $2$ by $1$ .

$f (1) = 5 {(2 - 5)}^{2}$

Subtract $5$ from $2$ .

$f (1) = 5 {(- 3)}^{2}$

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

$f (1) = 5 \cdot 9$

Multiply $5$ by $9$ .

$f (1) = 45$

The final answer is $45$ .

$45$

Convert $45$ to decimal.

$y = 45$

Step 3

Find the point at $x = 2$ .

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

$f (2) = 5 (2) {(2 (2) - 5)}^{2}$

Simplify the result.

Multiply $5$ by $2$ .

$f (2) = 10 {(2 (2) - 5)}^{2}$

Multiply $2$ by $2$ .

$f (2) = 10 {(4 - 5)}^{2}$

Subtract $5$ from $4$ .

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

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

$f (2) = 10 \cdot 1$

Multiply $10$ by $1$ .

$f (2) = 10$

The final answer is $10$ .

$10$

Convert $10$ to decimal.

$y = 10$

Step 4

Find the point at $x = 3$ .

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

$f (3) = 5 (3) {(2 (3) - 5)}^{2}$

Simplify the result.

Multiply $5$ by $3$ .

$f (3) = 15 {(2 (3) - 5)}^{2}$

Multiply $2$ by $3$ .

$f (3) = 15 {(6 - 5)}^{2}$

Subtract $5$ from $6$ .

$f (3) = 15 \cdot 1^{2}$

One to any power is one.

$f (3) = 15 \cdot 1$

Multiply $15$ by $1$ .

$f (3) = 15$

The final answer is $15$ .

$15$

Convert $15$ to decimal.

$y = 15$

Step 5

Find the point at $x = 4$ .

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

$f (4) = 5 (4) {(2 (4) - 5)}^{2}$

Simplify the result.

Multiply $5$ by $4$ .

$f (4) = 20 {(2 (4) - 5)}^{2}$

Multiply $2$ by $4$ .

$f (4) = 20 {(8 - 5)}^{2}$

Subtract $5$ from $8$ .

$f (4) = 20 \cdot 3^{2}$

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

$f (4) = 20 \cdot 9$

Multiply $20$ by $9$ .

$f (4) = 180$

The final answer is $180$ .

$180$

Convert $180$ to decimal.

$y = 180$

Step 6

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 45 \\ 2 & 10 \\ 3 & 15 \\ 4 & 180 \end{array}$

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 45 \\ 2 & 10 \\ 3 & 15 \\ 4 & 180 \end{array}$

Step 8

Graph f(x)=5x(2x-5)^2

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