Algebra Examples

$f (x) = - (x - 3) (x + 11)$

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 $x$ .

$0 = - (x - 3) (x + 11)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- (x - 3) (x + 11) = 0$ .

$- (x - 3) (x + 11) = 0$

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 $0$ .

$x - 3 = 0$

$x + 11 = 0$

Step 1.2.3

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

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Step 1.2.3.1

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

$x - 3 = 0$

Step 1.2.3.2

Add $3$ to both sides of the equation.

$x = 3$

Step 1.2.4

Set $x + 11$ equal to $0$ and solve for $x$ .

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Step 1.2.4.1

Set $x + 11$ equal to $0$ .

$x + 11 = 0$

Step 1.2.4.2

Subtract $11$ from both sides of the equation.

$x = - 11$

Step 1.2.5

The final solution is all the values that make $- (x - 3) (x + 11) = 0$ true.

$x = 3, - 11$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 11, 0)$

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 $y$ .

$y = - ((0) - 3) ((0) + 11)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - (0 - 3) ((0) + 11)$

Step 2.2.2

Remove parentheses.

$y = - (0 - 3) (0 + 11)$

Step 2.2.3

Remove parentheses.

$y = - ((0) - 3) ((0) + 11)$

Step 2.2.4

Simplify $- ((0) - 3) ((0) + 11)$ .

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Step 2.2.4.1

Subtract $3$ from $0$ .

$y = - - 3 ((0) + 11)$

Step 2.2.4.2

Multiply $- 1$ by $- 3$ .

$y = 3 ((0) + 11)$

Step 2.2.4.3

Add $0$ and $11$ .

$y = 3 \cdot 11$

Step 2.2.4.4

Multiply $3$ by $11$ .

$y = 33$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 33)$

Step 3

List the intersections.

x-intercept(s): $(3, 0), (- 11, 0)$

y-intercept(s): $(0, 33)$

Step 4