Algebra Examples

$x^{2} - 22 x$

Step 1

Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = 1$

$b = - 22$

$c = 0$

Step 2

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Step 3

Find the value of $d$ using the formula $d = \frac{b}{2 a}$ .

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Step 3.1

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = \frac{- 22}{2 \cdot 1}$

Step 3.2

Cancel the common factor of $- 22$ and $2$ .

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Step 3.2.1

Factor $2$ out of $- 22$ .

$d = \frac{2 \cdot - 11}{2 \cdot 1}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $2 \cdot 1$ .

$d = \frac{2 \cdot - 11}{2 (1)}$

Step 3.2.2.2

Cancel the common factor.

$d = \frac{2 \cdot - 11}{2 \cdot 1}$

Step 3.2.2.3

Rewrite the expression.

$d = \frac{- 11}{1}$

Step 3.2.2.4

Divide $- 11$ by $1$ .

$d = - 11$

Step 4

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

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Step 4.1

Substitute the values of $c$ , $b$ and $a$ into the formula $e = c - \frac{b^{2}}{4 a}$ .

$e = 0 - \frac{{(- 22)}^{2}}{4 \cdot 1}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Raise $- 22$ to the power of $2$ .

$e = 0 - \frac{484}{4 \cdot 1}$

Step 4.2.1.2

Multiply $4$ by $1$ .

$e = 0 - \frac{484}{4}$

Step 4.2.1.3

Divide $484$ by $4$ .

$e = 0 - 1 \cdot 121$

Step 4.2.1.4

Multiply $- 1$ by $121$ .

$e = 0 - 121$

Step 4.2.2

Subtract $121$ from $0$ .

$e = - 121$

Step 5

Substitute the values of $a$ , $d$ , and $e$ into the vertex form ${(x - 11)}^{2} - 121$ .

${(x - 11)}^{2} - 121$