Find the x and y Intercepts 4x^2(x+7)^5

$4 x^{2} {(x + 7)}^{5}$

Step 1

Write $4 x^{2} {(x + 7)}^{5}$ as an equation.

$y = 4 x^{2} {(x + 7)}^{5}$

Step 2

Find the x-intercepts.

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

$0 = 4 x^{2} {(x + 7)}^{5}$

Solve the equation.

Rewrite the equation as $4 x^{2} {(x + 7)}^{5} = 0$ .

$4 x^{2} {(x + 7)}^{5} = 0$

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

$x^{2} = 0$

${(x + 7)}^{5} = 0$

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set ${(x + 7)}^{5}$ equal to $0$ and solve for $x$ .

Set ${(x + 7)}^{5}$ equal to $0$ .

${(x + 7)}^{5} = 0$

Solve ${(x + 7)}^{5} = 0$ for $x$ .

Set the $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make $4 x^{2} {(x + 7)}^{5} = 0$ true.

$x = 0, - 7$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 7, 0)$

Step 3

Find the y-intercepts.

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

$y = 4 {(0)}^{2} {((0) + 7)}^{5}$

Solve the equation.

Remove parentheses.

$y = 4 \cdot (0^{2} {((0) + 7)}^{5})$

Remove parentheses.

$y = 4 \cdot (0^{2} {(0 + 7)}^{5})$

Remove parentheses.

$y = 4 {(0)}^{2} {((0) + 7)}^{5}$

Simplify $4 {(0)}^{2} {((0) + 7)}^{5}$ .

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

$y = 4 \cdot 0 {((0) + 7)}^{5}$

Multiply $4$ by $0$ .

$y = 0 {((0) + 7)}^{5}$

Add $0$ and $7$ .

$y = 0 \cdot 7^{5}$

Raise $7$ to the power of $5$ .

$y = 0 \cdot 16807$

Multiply $0$ by $16807$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(0, 0), (- 7, 0)$

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

Step 5

Find the x and y Intercepts 4x^2(x+7)^5

Related Questions

Support LCMGCF.com by disabling your adblocker.