Find the x and y Intercepts h(x)=x^2+9x+18

$h (x) = x^{2} + 9 x + 18$

Step 1

Find the x-intercepts.

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

$0 = x^{2} + 9 x + 18$

Solve the equation.

Rewrite the equation as $x^{2} + 9 x + 18 = 0$ .

$x^{2} + 9 x + 18 = 0$

Factor $x^{2} + 9 x + 18$ 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 $18$ and whose sum is $9$ .

$3, 6$

Write the factored form using these integers.

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

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

$x + 3 = 0$

$x + 6 = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x + 3) (x + 6) = 0$ true.

$x = - 3, - 6$

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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

$y = {(0)}^{2} + 9 (0) + 18$

Solve the equation.

Remove parentheses.

$y = 0^{2} + 9 (0) + 18$

Remove parentheses.

$y = {(0)}^{2} + 9 (0) + 18$

Simplify ${(0)}^{2} + 9 (0) + 18$ .

Simplify each term.

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

$y = 0 + 9 (0) + 18$

Multiply $9$ by $0$ .

$y = 0 + 0 + 18$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 18$

Add $0$ and $18$ .

$y = 18$

y-intercept(s) in point form.

y-intercept(s): $(0, 18)$

Step 3

List the intersections.

x-intercept(s): $(- 3, 0), (- 6, 0)$

y-intercept(s): $(0, 18)$

Step 4

Find the x and y Intercepts h(x)=x^2+9x+18

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