Precalculus Examples

$x^{2} = 28 y$

Rewrite the equation in vertex form.

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Isolate $y$ to the left side of the equation.

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Rewrite the equation as $28 y = x^{2}$ .

$28 y = x^{2}$

Divide each term in $28 y = x^{2}$ by $28$ and simplify.

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Divide each term in $28 y = x^{2}$ by $28$ .

$\frac{28 y}{28} = \frac{x^{2}}{28}$

Simplify the left side.

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Cancel the common factor of $28$ .

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Cancel the common factor.

$\frac{28 y}{28} = \frac{x^{2}}{28}$

Divide $y$ by $1$ .

$y = \frac{x^{2}}{28}$

Complete the square for $\frac{x^{2}}{28}$ .

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

$a = \frac{1}{28}$

$b = 0$

$c = 0$

Consider the vertex form of a parabola.

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

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

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

$d = \frac{0}{2 (\frac{1}{28})}$

Simplify the right side.

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Cancel the common factor of $0$ and $2$ .

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Factor $2$ out of $0$ .

$d = \frac{2 (0)}{2 (\frac{1}{28})}$

Cancel the common factors.

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Cancel the common factor.

$d = \frac{2 \cdot 0}{2 (\frac{1}{28})}$

Rewrite the expression.

$d = \frac{0}{\frac{1}{28}}$

Multiply the numerator by the reciprocal of the denominator.

$d = 0 \cdot 28$

Multiply $0$ by $28$ .

$d = 0$

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

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

$e = 0 - \frac{0^{2}}{4 (\frac{1}{28})}$

Simplify the right side.

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Simplify each term.

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

$e = 0 - \frac{0}{4 (\frac{1}{28})}$

Combine $4$ and $\frac{1}{28}$ .

$e = 0 - \frac{0}{\frac{4}{28}}$

Cancel the common factor of $4$ and $28$ .

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Factor $4$ out of $4$ .

$e = 0 - \frac{0}{\frac{4 (1)}{28}}$

Cancel the common factors.

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Factor $4$ out of $28$ .

$e = 0 - \frac{0}{\frac{4 \cdot 1}{4 \cdot 7}}$

Cancel the common factor.

$e = 0 - \frac{0}{\frac{4 \cdot 1}{4 \cdot 7}}$

Rewrite the expression.

$e = 0 - \frac{0}{\frac{1}{7}}$

Multiply the numerator by the reciprocal of the denominator.

$e = 0 - (0 \cdot 7)$

Multiply $0$ by $7$ .

$e = 0 - 0$

Multiply $- 1$ by $0$ .

$e = 0 + 0$

Add $0$ and $0$ .

$e = 0$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $\frac{1}{28} x^{2}$ .

$\frac{1}{28} x^{2}$

Set $y$ equal to the new right side.

$y = \frac{1}{28} x^{2}$

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = \frac{1}{28}$

$h = 0$

$k = 0$

Find the vertex $(h, k)$ .

$(0, 0)$