Precalculus Examples

${(x - 3)}^{2} = 8 (y + 1)$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Rewrite the equation as $8 (y + 1) = {(x - 3)}^{2}$ .

$8 (y + 1) = {(x - 3)}^{2}$

Step 1.2

Divide each term in $8 (y + 1) = {(x - 3)}^{2}$ by $8$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $8 (y + 1) = {(x - 3)}^{2}$ by $8$ .

$\frac{8 (y + 1)}{8} = \frac{{(x - 3)}^{2}}{8}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 (y + 1)}{8} = \frac{{(x - 3)}^{2}}{8}$

Step 1.2.2.1.2

Divide $y + 1$ by $1$ .

$y + 1 = \frac{{(x - 3)}^{2}}{8}$

Step 1.3

Subtract $1$ from both sides of the equation.

$y = \frac{{(x - 3)}^{2}}{8} - 1$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

Reorder terms.

$y = \frac{1}{8} \cdot {(x - 3)}^{2} - 1$

Step 4