Find the x and y Intercepts y=5x-x^2

$y = 5 x - x^{2}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 5 x - x^{2}$

Solve the equation.

Rewrite the equation as $5 x - x^{2} = 0$ .

$5 x - x^{2} = 0$

Factor the left side of the equation.

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$5 u - u^{2} = 0$

Factor $u$ out of $5 u - u^{2}$ .

Factor $u$ out of $5 u$ .

$u \cdot 5 - u^{2} = 0$

Factor $u$ out of $- u^{2}$ .

$u \cdot 5 + u (- u) = 0$

Factor $u$ out of $u \cdot 5 + u (- u)$ .

$u (5 - u) = 0$

Replace all occurrences of $u$ with $x$ .

$x (5 - x) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$5 - x = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $5 - x$ equal to $0$ and solve for $x$ .

Set $5 - x$ equal to $0$ .

$5 - x = 0$

Solve $5 - x = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$- x = - 5$

Divide each term in $- x = - 5$ by $- 1$ and simplify.

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x = 5$

The final solution is all the values that make $x (5 - x) = 0$ true.

$x = 0, 5$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (5, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Simplify $5 (0) - {(0)}^{2}$ .

Simplify each term.

Multiply $5$ by $0$ .

$y = 0 - {(0)}^{2}$

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

$y = 0 - 0$

Multiply $- 1$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

x-intercept(s): $(0, 0), (5, 0)$

y-intercept(s): $(0, 0)$

Step 4

Find the x and y Intercepts y=5x-x^2

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