Find the x and y Intercepts P(x)=-x^2+4x

$P (x) = - x^{2} + 4 x$

Step 1

Find the x-intercepts.

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

$0 = - x^{2} + 4 x$

Solve the equation.

Rewrite the equation as $- x^{2} + 4 x = 0$ .

$- x^{2} + 4 x = 0$

Factor $- x$ out of $- x^{2} + 4 x$ .

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

$- x \cdot x + 4 x = 0$

Factor $- x$ out of $4 x$ .

$- x \cdot x - x \cdot - 4 = 0$

Factor $- x$ out of $- x (x) - x (- 4)$ .

$- x (x - 4) = 0$

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

$x = 0$

$x - 4 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $- x (x - 4) = 0$ true.

$x = 0, 4$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (4, 0)$

Step 2

Find the y-intercepts.

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

$y = - {(0)}^{2} + 4 (0)$

Solve the equation.

Remove parentheses.

$y = - 0^{2} + 4 (0)$

Remove parentheses.

$y = - {(0)}^{2} + 4 (0)$

Simplify $- {(0)}^{2} + 4 (0)$ .

Simplify each term.

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

$y = - 0 + 4 (0)$

Multiply $- 1$ by $0$ .

$y = 0 + 4 (0)$

Multiply $4$ 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): $(0, 0), (4, 0)$

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

Step 4

Find the x and y Intercepts P(x)=-x^2+4x

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