Find the x and y Intercepts f(x)=6+5x+x^2

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

Step 1

Find the x-intercepts.

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

$0 = 6 + 5 x + x^{2}$

Solve the equation.

Rewrite the equation as $6 + 5 x + x^{2} = 0$ .

$6 + 5 x + x^{2} = 0$

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

$2, 3$

Write the factored form using these integers.

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

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

$x + 2 = 0$

$x + 3 = 0$

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.

$x = - 2$

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.

$x = - 3$

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

$x = - 2, - 3$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0), (- 3, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Simplify $6 + 5 (0) + {(0)}^{2}$ .

Simplify each term.

Multiply $5$ by $0$ .

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

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

$y = 6 + 0 + 0$

Simplify by adding numbers.

Add $6$ and $0$ .

$y = 6 + 0$

Add $6$ and $0$ .

$y = 6$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 2, 0), (- 3, 0)$

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

Step 4

Find the x and y Intercepts f(x)=6+5x+x^2

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