Find the x and y Intercepts y=(4x^2+12x)/(x+7)

$y = \frac{4 x^{2} + 12 x}{x + 7}$

Step 1

Find the x-intercepts.

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

$0 = \frac{4 x^{2} + 12 x}{x + 7}$

Solve the equation.

Set the numerator equal to zero.

$4 x^{2} + 12 x = 0$

Solve the equation for $x$ .

Factor $4 x$ out of $4 x^{2} + 12 x$ .

Factor $4 x$ out of $4 x^{2}$ .

$4 x (x) + 12 x = 0$

Factor $4 x$ out of $12 x$ .

$4 x (x) + 4 x (3) = 0$

Factor $4 x$ out of $4 x (x) + 4 x (3)$ .

$4 x (x + 3) = 0$

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

$x = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

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.

$x = - 3$

The final solution is all the values that make $4 x (x + 3) = 0$ true.

$x = 0, - 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{4 {(0)}^{2} + 12 (0)}{(0) + 7}$

Solve the equation.

Remove parentheses.

$y = \frac{4 \cdot 0^{2} + 12 (0)}{(0) + 7}$

Remove parentheses.

$y = \frac{4 \cdot 0^{2} + 12 (0)}{0 + 7}$

Remove parentheses.

$y = \frac{4 {(0)}^{2} + 12 (0)}{(0) + 7}$

Simplify $\frac{4 {(0)}^{2} + 12 (0)}{(0) + 7}$ .

Simplify the numerator.

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

$y = \frac{4 \cdot 0 + 12 (0)}{0 + 7}$

Multiply $4$ by $0$ .

$y = \frac{0 + 12 (0)}{0 + 7}$

Multiply $12$ by $0$ .

$y = \frac{0 + 0}{0 + 7}$

Add $0$ and $0$ .

$y = \frac{0}{0 + 7}$

Simplify the expression.

Add $0$ and $7$ .

$y = \frac{0}{7}$

Divide $0$ by $7$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts y=(4x^2+12x)/(x+7)

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