Find the x and y Intercepts y=(4-x)(x-3)

$y = (4 - x) (x - 3)$

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$4 - x = 0$

$x - 3 = 0$

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

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

$4 - x = 0$

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

Subtract $4$ from both sides of the equation.

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

$x = 4, 3$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (3, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Simplify $(4 - (0)) ((0) - 3)$ .

Subtract $0$ from $4$ .

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

Subtract $3$ from $0$ .

$y = 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$y = - 12$

y-intercept(s) in point form.

y-intercept(s): $(0, - 12)$

List the intersections.

x-intercept(s): $(4, 0), (3, 0)$

y-intercept(s): $(0, - 12)$

Find the x and y Intercepts y=(4-x)(x-3)

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