Precalculus Examples

$f (x) = 2 (x + 1) (x - 2)$

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 $x$ .

$0 = 2 (x + 1) (x - 2)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $2 (x + 1) (x - 2) = 0$ .

$2 (x + 1) (x - 2) = 0$

Step 1.2.2

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

$x + 1 = 0$

$x - 2 = 0$

Step 1.2.3

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

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Step 1.2.3.1

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

$x + 1 = 0$

Step 1.2.3.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 1.2.4

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

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Step 1.2.4.1

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

$x - 2 = 0$

Step 1.2.4.2

Add $2$ to both sides of the equation.

$x = 2$

Step 1.2.5

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

$x = - 1, 2$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0), (2, 0)$

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 $y$ .

$y = 2 ((0) + 1) ((0) - 2)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 2 (0 + 1) ((0) - 2)$

Step 2.2.2

Remove parentheses.

$y = 2 (0 + 1) (0 - 2)$

Step 2.2.3

Remove parentheses.

$y = 2 ((0) + 1) ((0) - 2)$

Step 2.2.4

Simplify $2 ((0) + 1) ((0) - 2)$ .

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Step 2.2.4.1

Add $0$ and $1$ .

$y = 2 \cdot 1 ((0) - 2)$

Step 2.2.4.2

Multiply $2$ by $1$ .

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

Step 2.2.4.3

Subtract $2$ from $0$ .

$y = 2 \cdot - 2$

Step 2.2.4.4

Multiply $2$ by $- 2$ .

$y = - 4$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 1, 0), (2, 0)$

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

Step 4