Algebra Examples

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

Step 1

Find the x-intercepts.

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Step 1.1

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

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

Step 1.2

Solve the equation.

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Step 1.2.1

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

$x - 4 = 0$

$x + 2 = 0$

Step 1.2.2

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

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Step 1.2.2.1

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

$x - 4 = 0$

Step 1.2.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 1.2.3

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

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Step 1.2.3.1

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

$x + 2 = 0$

Step 1.2.3.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 1.2.4

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

$x = 4, - 2$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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Step 2.1

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

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

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $y = ((0) - 4) ((0) + 2)$ .

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

Step 2.2.2

Simplify $((0) - 4) ((0) + 2)$ .

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Step 2.2.2.1

Subtract $4$ from $0$ .

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

Step 2.2.2.2

Add $0$ and $2$ .

$y = - 4 \cdot 2$

Step 2.2.2.3

Multiply $- 4$ by $2$ .

$y = - 8$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 8)$

Step 4