Algebra Examples

$f (x) = x^{2} + 4 x - 12$

Step 1

Find the x-intercepts.

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

$0 = x^{2} + 4 x - 12$

Solve the equation.

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Rewrite the equation as $x^{2} + 4 x - 12 = 0$ .

$x^{2} + 4 x - 12 = 0$

Factor $x^{2} + 4 x - 12$ using the AC method.

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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 $- 12$ and whose sum is $4$ .

$- 2, 6$

Write the factored form using these integers.

$(x - 2) (x + 6) = 0$

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

$x - 2 = 0$

$x + 6 = 0$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x + 6$ equal to $0$ and solve for $x$ .

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Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x - 2) (x + 6) = 0$ true.

$x = 2, - 6$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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

$y = {(0)}^{2} + 4 (0) - 12$

Solve the equation.

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Remove parentheses.

$y = 0^{2} + 4 (0) - 12$

Remove parentheses.

$y = {(0)}^{2} + 4 (0) - 12$

Simplify ${(0)}^{2} + 4 (0) - 12$ .

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Simplify each term.

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Raising $0$ to any positive power yields $0$ .

$y = 0 + 4 (0) - 12$

Multiply $4$ by $0$ .

$y = 0 + 0 - 12$

Simplify by adding and subtracting.

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Add $0$ and $0$ .

$y = 0 - 12$

Subtract $12$ from $0$ .

$y = - 12$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(2, 0), (- 6, 0)$

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

Step 4