Algebra Examples

$y = x^{2} + 4$

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

$a = 1, b = 0, c = 4$

Consider the vertex form of a parabola.

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

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

$d = \frac{0}{2 (1)}$

Reduce the expression by cancelling the common factors.

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Factor $2$ out of $0$ .

$d = \frac{2 (0)}{2 (1)}$

Cancel the common factors.

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Cancel the common factor.

$d = \frac{2 \cdot 0}{2 \cdot 1}$

Rewrite the expression.

$d = \frac{0}{1}$

Divide $0$ by $1$ .

$d = 0$

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

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Simplify each term.

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

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

Multiply $4$ by $1$ .

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

Divide $0$ by $4$ .

$e = 4 - 0$

Multiply $- 1$ by $0$ .

$e = 4 + 0$

Add $4$ and $0$ .

$e = 4$

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

${(x + 0)}^{2} + 4$

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