Find the x and y Intercepts -4x^2+8x

$- 4 x^{2} + 8 x$

Step 1

Write $- 4 x^{2} + 8 x$ as an equation.

$y = - 4 x^{2} + 8 x$

Step 2

Find the x-intercepts.

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

$0 = - 4 x^{2} + 8 x$

Solve the equation.

Rewrite the equation as $- 4 x^{2} + 8 x = 0$ .

$- 4 x^{2} + 8 x = 0$

Factor $- 4 x$ out of $- 4 x^{2} + 8 x$ .

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

$- 4 x \cdot x + 8 x = 0$

Factor $- 4 x$ out of $8 x$ .

$- 4 x \cdot x - 4 x \cdot - 2 = 0$

Factor $- 4 x$ out of $- 4 x (x) - 4 x (- 2)$ .

$- 4 x (x - 2) = 0$

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

$x = 0$

$x - 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $- 4 x (x - 2) = 0$ true.

$x = 0, 2$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (2, 0)$

Step 3

Find the y-intercepts.

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

$y = - 4 {(0)}^{2} + 8 (0)$

Solve the equation.

Remove parentheses.

$y = - 4 \cdot 0^{2} + 8 (0)$

Remove parentheses.

$y = - 4 {(0)}^{2} + 8 (0)$

Simplify $- 4 {(0)}^{2} + 8 (0)$ .

Simplify each term.

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

$y = - 4 \cdot 0 + 8 (0)$

Multiply $- 4$ by $0$ .

$y = 0 + 8 (0)$

Multiply $8$ 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): $(0, 0), (2, 0)$

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

Step 5

Find the x and y Intercepts -4x^2+8x

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