Find the x and y Intercepts y=2x^2+x

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

$x (2 x) + x = 0$

Raise $x$ to the power of $1$ .

$x (2 x) + x = 0$

Factor $x$ out of $x^{1}$ .

$x (2 x) + x \cdot 1 = 0$

Factor $x$ out of $x (2 x) + x \cdot 1$ .

$x (2 x + 1) = 0$

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

$x = 0$

$2 x + 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $2 x + 1$ equal to $0$ and solve for $x$ .

Set $2 x + 1$ equal to $0$ .

$2 x + 1 = 0$

Solve $2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

The final solution is all the values that make $x (2 x + 1) = 0$ true.

$x = 0, - \frac{1}{2}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- \frac{1}{2}, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

$y = 2 \cdot 0^{2} + 0$

Remove parentheses.

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

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

Simplify each term.

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

$y = 2 \cdot 0 + 0$

Multiply $2$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (- \frac{1}{2}, 0)$

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

Find the x and y Intercepts y=2x^2+x

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