Precalculus Examples

${(y - 9)}^{2} = - 4 (x - 2)$

Step 1

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

Tap for more steps...

Step 1.1

Rewrite the equation as $- 4 (x - 2) = {(y - 9)}^{2}$ .

$- 4 (x - 2) = {(y - 9)}^{2}$

Step 1.2

Divide each term in $- 4 (x - 2) = {(y - 9)}^{2}$ by $- 4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 4 (x - 2) = {(y - 9)}^{2}$ by $- 4$ .

$\frac{- 4 (x - 2)}{- 4} = \frac{{(y - 9)}^{2}}{- 4}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 (x - 2)}{- 4} = \frac{{(y - 9)}^{2}}{- 4}$

Step 1.2.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 = \frac{{(y - 9)}^{2}}{- 4}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Move the negative in front of the fraction.

$x - 2 = - \frac{{(y - 9)}^{2}}{4}$

Step 1.3

Add $2$ to both sides of the equation.

$x = - \frac{{(y - 9)}^{2}}{4} + 2$

Step 1.4

Reorder terms.

$x = - \frac{1}{4} \cdot {(y - 9)}^{2} + 2$

Step 2

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

$a = - \frac{1}{4}$

$h = 2$

$k = 9$

Step 3

Find the vertex $(h, k)$ .

$(2, 9)$

Step 4