Find the x and y Intercepts f(x)=-5(x+2)^2(5x+1)

$f (x) = - 5 {(x + 2)}^{2} (5 x + 1)$

Find the x-intercepts.

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

$0 = - 5 {(x + 2)}^{2} (5 x + 1)$

Solve the equation.

Rewrite the equation as $- 5 {(x + 2)}^{2} (5 x + 1) = 0$ .

$- 5 {(x + 2)}^{2} (5 x + 1) = 0$

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

${(x + 2)}^{2} = 0$

$5 x + 1 = 0$

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

Set ${(x + 2)}^{2}$ equal to $0$ .

${(x + 2)}^{2} = 0$

Solve ${(x + 2)}^{2} = 0$ for $x$ .

Set the $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $5 x + 1$ equal to $0$ and solve for $x$ .

Set $5 x + 1$ equal to $0$ .

$5 x + 1 = 0$

Solve $5 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$5 x = - 1$

Divide each term in $5 x = - 1$ by $5$ and simplify.

Divide each term in $5 x = - 1$ by $5$ .

$\frac{5 x}{5} = \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 1}{5}$

Divide $x$ by $1$ .

$x = \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

The final solution is all the values that make $- 5 {(x + 2)}^{2} (5 x + 1) = 0$ true.

$x = - 2, - \frac{1}{5}$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0), (- \frac{1}{5}, 0)$

Find the y-intercepts.

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

$y = - 5 {((0) + 2)}^{2} (5 (0) + 1)$

Solve the equation.

Remove parentheses.

$y = - 5 {(0 + 2)}^{2} (5 (0) + 1)$

Remove parentheses.

$y = - 5 {((0) + 2)}^{2} (5 (0) + 1)$

Simplify $- 5 {((0) + 2)}^{2} (5 (0) + 1)$ .

Add $0$ and $2$ .

$y = - 5 \cdot 2^{2} (5 (0) + 1)$

Raise $2$ to the power of $2$ .

$y = - 5 \cdot 4 (5 (0) + 1)$

Multiply $- 5$ by $4$ .

$y = - 20 (5 (0) + 1)$

Multiply $5$ by $0$ .

$y = - 20 (0 + 1)$

Add $0$ and $1$ .

$y = - 20 \cdot 1$

Multiply $- 20$ by $1$ .

$y = - 20$

y-intercept(s) in point form.

y-intercept(s): $(0, - 20)$

List the intersections.

x-intercept(s): $(- 2, 0), (- \frac{1}{5}, 0)$

y-intercept(s): $(0, - 20)$

Find the x and y Intercepts f(x)=-5(x+2)^2(5x+1)

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