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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

Factor the left side of the equation.

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

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

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 6$ .

$3 (x^{2}) + 3 x + 3 \cdot - 2 = 0$

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

$3 (x^{2} + x) + 3 \cdot - 2 = 0$

Factor $3$ out of $3 (x^{2} + x) + 3 \cdot - 2$ .

$3 (x^{2} + x - 2) = 0$

Factor.

Factor $x^{2} + x - 2$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Write the factored form using these integers.

$3 ((x - 1) (x + 2)) = 0$

Remove unnecessary parentheses.

$3 (x - 1) (x + 2) = 0$

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

$x - 1 = 0$

$x + 2 = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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 $3 (x - 1) (x + 2) = 0$ true.

$x = 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

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

Multiply $3$ by $0$ .

$y = 0 + 3 (0) - 6$

Multiply $3$ by $0$ .

$y = 0 + 0 - 6$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

y-intercept(s) in point form.

y-intercept(s): $(0, - 6)$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (- 2, 0)$

y-intercept(s): $(0, - 6)$

Step 4

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

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