Find the x and y Intercepts y=1/2(x+4)(x-2)

$y = \frac{1}{2} (x + 4) (x - 2)$

Find the x-intercepts.

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

$0 = \frac{1}{2} \cdot ((x + 4) (x - 2))$

Solve the equation.

Rewrite the equation as $\frac{1}{2} \cdot ((x + 4) (x - 2)) = 0$ .

$\frac{1}{2} \cdot ((x + 4) (x - 2)) = 0$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot ((x + 4) (x - 2))) = 2 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot ((x + 4) (x - 2)))$ .

Expand $(x + 4) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$2 (\frac{1}{2} \cdot (x (x - 2) + 4 (x - 2))) = 2 \cdot 0$

Apply the distributive property.

$2 (\frac{1}{2} \cdot (x \cdot x + x \cdot - 2 + 4 (x - 2))) = 2 \cdot 0$

Apply the distributive property.

$2 (\frac{1}{2} \cdot (x \cdot x + x \cdot - 2 + 4 x + 4 \cdot - 2)) = 2 \cdot 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 (\frac{1}{2} \cdot (x^{2} + x \cdot - 2 + 4 x + 4 \cdot - 2)) = 2 \cdot 0$

Move $- 2$ to the left of $x$ .

$2 (\frac{1}{2} \cdot (x^{2} - 2 \cdot x + 4 x + 4 \cdot - 2)) = 2 \cdot 0$

Multiply $4$ by $- 2$ .

$2 (\frac{1}{2} \cdot (x^{2} - 2 x + 4 x - 8)) = 2 \cdot 0$

Add $- 2 x$ and $4 x$ .

$2 (\frac{1}{2} \cdot (x^{2} + 2 x - 8)) = 2 \cdot 0$

Apply the distributive property.

$2 (\frac{1}{2} x^{2} + \frac{1}{2} (2 x) + \frac{1}{2} \cdot - 8) = 2 \cdot 0$

Simplify.

Combine $\frac{1}{2}$ and $x^{2}$ .

$2 (\frac{x^{2}}{2} + \frac{1}{2} (2 x) + \frac{1}{2} \cdot - 8) = 2 \cdot 0$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$2 (\frac{x^{2}}{2} + \frac{1}{2} (2 (x)) + \frac{1}{2} \cdot - 8) = 2 \cdot 0$

Cancel the common factor.

$2 (\frac{x^{2}}{2} + \frac{1}{2} (2 x) + \frac{1}{2} \cdot - 8) = 2 \cdot 0$

Rewrite the expression.

$2 (\frac{x^{2}}{2} + x + \frac{1}{2} \cdot - 8) = 2 \cdot 0$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$2 (\frac{x^{2}}{2} + x + \frac{1}{2} \cdot (2 (- 4))) = 2 \cdot 0$

Cancel the common factor.

$2 (\frac{x^{2}}{2} + x + \frac{1}{2} \cdot (2 \cdot - 4)) = 2 \cdot 0$

Rewrite the expression.

$2 (\frac{x^{2}}{2} + x - 4) = 2 \cdot 0$

Apply the distributive property.

$2 \frac{x^{2}}{2} + 2 x + 2 \cdot - 4 = 2 \cdot 0$

Simplify.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x^{2}}{2} + 2 x + 2 \cdot - 4 = 2 \cdot 0$

Rewrite the expression.

$x^{2} + 2 x + 2 \cdot - 4 = 2 \cdot 0$

Multiply $2$ by $- 4$ .

$x^{2} + 2 x - 8 = 2 \cdot 0$

Simplify the right side.

Multiply $2$ by $0$ .

$x^{2} + 2 x - 8 = 0$

Factor $x^{2} + 2 x - 8$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $2$ .

$- 2, 4$

Write the factored form using these integers.

$(x - 2) (x + 4) = 0$

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

$x - 2 = 0$

$x + 4 = 0$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $(x - 2) (x + 4) = 0$ true.

$x = 2, - 4$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 4, 0)$

Find the y-intercepts.

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

$y = \frac{1}{2} \cdot (((0) + 4) ((0) - 2))$

Solve the equation.

Remove parentheses.

$y = \frac{1}{2} \cdot ((0 + 4) ((0) - 2))$

Remove parentheses.

$y = \frac{1}{2} \cdot ((0 + 4) (0 - 2))$

Remove parentheses.

$y = \frac{1}{2} \cdot ((0 + 4) (0 - 2))$

Remove parentheses.

$y = \frac{1}{2} \cdot (((0) + 4) ((0) - 2))$

Simplify $\frac{1}{2} \cdot (((0) + 4) ((0) - 2))$ .

Add $0$ and $4$ .

$y = \frac{1}{2} \cdot (4 ((0) - 2))$

Cancel the common factor of $2$ .

Factor $2$ out of $4 ((0) - 2)$ .

$y = \frac{1}{2} \cdot (2 (2 ((0) - 2)))$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 (2 ((0) - 2)))$

Rewrite the expression.

$y = 2 ((0) - 2)$

Simplify the expression.

Subtract $2$ from $0$ .

$y = 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

List the intersections.

x-intercept(s): $(2, 0), (- 4, 0)$

y-intercept(s): $(0, - 4)$

Find the x and y Intercepts y=1/2(x+4)(x-2)

Related Questions

Support LCMGCF.com by disabling your adblocker.