Find the x and y Intercepts -x^2+12x

$- x^{2} + 12 x$

Step 1

Write $- x^{2} + 12 x$ as an equation.

$y = - x^{2} + 12 x$

Step 2

Find the x-intercepts.

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

$0 = - x^{2} + 12 x$

Solve the equation.

Rewrite the equation as $- x^{2} + 12 x = 0$ .

$- x^{2} + 12 x = 0$

Factor $- x$ out of $- x^{2} + 12 x$ .

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

$- x \cdot x + 12 x = 0$

Factor $- x$ out of $12 x$ .

$- x \cdot x - x \cdot - 12 = 0$

Factor $- x$ out of $- x (x) - x (- 12)$ .

$- x (x - 12) = 0$

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

$x = 0$

$x - 12 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 12$ equal to $0$ and solve for $x$ .

Set $x - 12$ equal to $0$ .

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

The final solution is all the values that make $- x (x - 12) = 0$ true.

$x = 0, 12$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (12, 0)$

Step 3

Find the y-intercepts.

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

$y = - {(0)}^{2} + 12 (0)$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 12 (0)$

Remove parentheses.

$y = - {(0)}^{2} + 12 (0)$

Simplify $- {(0)}^{2} + 12 (0)$ .

Simplify each term.

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

$y = - 0 + 12 (0)$

Multiply $- 1$ by $0$ .

$y = 0 + 12 (0)$

Multiply $12$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(0, 0), (12, 0)$

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

Step 5

Find the x and y Intercepts -x^2+12x

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