Find the x and y Intercepts f(x)=-(x+3)(4x-5)(x-1)

$f (x) = - (x + 3) (4 x - 5) (x - 1)$

Find the x-intercepts.

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

$0 = - (x + 3) (4 x - 5) (x - 1)$

Solve the equation.

Rewrite the equation as $- (x + 3) (4 x - 5) (x - 1) = 0$ .

$- (x + 3) (4 x - 5) (x - 1) = 0$

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

$x + 3 = 0$

$4 x - 5 = 0$

$x - 1 = 0$

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 $4 x - 5$ equal to $0$ and solve for $x$ .

Set $4 x - 5$ equal to $0$ .

$4 x - 5 = 0$

Solve $4 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$4 x = 5$

Divide each term in $4 x = 5$ by $4$ and simplify.

Divide each term in $4 x = 5$ by $4$ .

$\frac{4 x}{4} = \frac{5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{5}{4}$

Divide $x$ by $1$ .

$x = \frac{5}{4}$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $- (x + 3) (4 x - 5) (x - 1) = 0$ true.

$x = - 3, \frac{5}{4}, 1$

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0), (\frac{5}{4}, 0), (1, 0)$

Find the y-intercepts.

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

$y = - ((0) + 3) (4 (0) - 5) ((0) - 1)$

Solve the equation.

Remove parentheses.

$y = - (0 + 3) (4 (0) - 5) ((0) - 1)$

Remove parentheses.

$y = - (0 + 3) (4 (0) - 5) (0 - 1)$

Remove parentheses.

$y = - ((0) + 3) (4 (0) - 5) ((0) - 1)$

Simplify $- ((0) + 3) (4 (0) - 5) ((0) - 1)$ .

Add $0$ and $3$ .

$y = - 1 \cdot 3 (4 (0) - 5) ((0) - 1)$

Multiply $- 1$ by $3$ .

$y = - 3 (4 (0) - 5) ((0) - 1)$

Multiply $4$ by $0$ .

$y = - 3 (0 - 5) ((0) - 1)$

Subtract $5$ from $0$ .

$y = - 3 \cdot - 5 ((0) - 1)$

Multiply $- 3$ by $- 5$ .

$y = 15 ((0) - 1)$

Subtract $1$ from $0$ .

$y = 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$y = - 15$

y-intercept(s) in point form.

y-intercept(s): $(0, - 15)$

List the intersections.

x-intercept(s): $(- 3, 0), (\frac{5}{4}, 0), (1, 0)$

y-intercept(s): $(0, - 15)$

Find the x and y Intercepts f(x)=-(x+3)(4x-5)(x-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.