Trigonometry Examples

$y = x^{2} - 2 x - 8$

Step 1

Set $x^{2} - 2 x - 8$ equal to $0$ .

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

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

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 $- 2$ .

$- 4, 2$

Step 2.1.2

Write the factored form using these integers.

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

Step 2.2

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

$x - 4 = 0$

$x + 2 = 0$

Step 2.3

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

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Step 2.3.1

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

$x - 4 = 0$

Step 2.3.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.4

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

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Step 2.4.1

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

$x + 2 = 0$

Step 2.4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 2.5

The final solution is all the values that make $(x - 4) (x + 2) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 4$ (Multiplicity of $1$ )

$x = - 2$ (Multiplicity of $1$ )

$x = 4$ (Multiplicity of $1$ )

$x = - 2$ (Multiplicity of $1$ )

Step 3