Find the x and y Intercepts y=3x^2+18x+15

$y = 3 x^{2} + 18 x + 15$

Find the x-intercepts.

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

$0 = 3 x^{2} + 18 x + 15$

Solve the equation.

Rewrite the equation as $3 x^{2} + 18 x + 15 = 0$ .

$3 x^{2} + 18 x + 15 = 0$

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} + 18 x + 15$ .

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

$3 (x^{2}) + 18 x + 15 = 0$

Factor $3$ out of $18 x$ .

$3 (x^{2}) + 3 (6 x) + 15 = 0$

Factor $3$ out of $15$ .

$3 x^{2} + 3 (6 x) + 3 \cdot 5 = 0$

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

$3 (x^{2} + 6 x) + 3 \cdot 5 = 0$

Factor $3$ out of $3 (x^{2} + 6 x) + 3 \cdot 5$ .

$3 (x^{2} + 6 x + 5) = 0$

Factor.

Factor $x^{2} + 6 x + 5$ 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 $5$ and whose sum is $6$ .

$1, 5$

Write the factored form using these integers.

$3 ((x + 1) (x + 5)) = 0$

Remove unnecessary parentheses.

$3 (x + 1) (x + 5) = 0$

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

$x + 1 = 0$

$x + 5 = 0$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $3 (x + 1) (x + 5) = 0$ true.

$x = - 1, - 5$

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0), (- 5, 0)$

Find the y-intercepts.

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

$y = 3 {(0)}^{2} + 18 (0) + 15$

Solve the equation.

Remove parentheses.

$y = 3 \cdot 0^{2} + 18 (0) + 15$

Remove parentheses.

$y = 3 {(0)}^{2} + 18 (0) + 15$

Simplify $3 {(0)}^{2} + 18 (0) + 15$ .

Simplify each term.

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

$y = 3 \cdot 0 + 18 (0) + 15$

Multiply $3$ by $0$ .

$y = 0 + 18 (0) + 15$

Multiply $18$ by $0$ .

$y = 0 + 0 + 15$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 15$

Add $0$ and $15$ .

$y = 15$

y-intercept(s) in point form.

y-intercept(s): $(0, 15)$

List the intersections.

x-intercept(s): $(- 1, 0), (- 5, 0)$

y-intercept(s): $(0, 15)$

Find the x and y Intercepts y=3x^2+18x+15

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