Find the x and y Intercepts y=3x^2+6x

$y = 3 x^{2} + 6 x$

Step 1

Find the x-intercepts.

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

$0 = 3 x^{2} + 6 x$

Solve the equation.

Rewrite the equation as $3 x^{2} + 6 x = 0$ .

$3 x^{2} + 6 x = 0$

Factor $3 x$ out of $3 x^{2} + 6 x$ .

Factor $3 x$ out of $3 x^{2}$ .

$3 x (x) + 6 x = 0$

Factor $3 x$ out of $6 x$ .

$3 x (x) + 3 x (2) = 0$

Factor $3 x$ out of $3 x (x) + 3 x (2)$ .

$3 x (x + 2) = 0$

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 $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $3 x (x + 2) = 0$ true.

$x = 0, - 2$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = 3 {(0)}^{2} + 6 (0)$

Solve the equation.

Remove parentheses.

$y = 3 \cdot 0^{2} + 6 (0)$

Remove parentheses.

$y = 3 {(0)}^{2} + 6 (0)$

Simplify $3 {(0)}^{2} + 6 (0)$ .

Simplify each term.

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

$y = 3 \cdot 0 + 6 (0)$

Multiply $3$ by $0$ .

$y = 0 + 6 (0)$

Multiply $6$ 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): $(0, 0), (- 2, 0)$

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

Step 4

Find the x and y Intercepts y=3x^2+6x

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