Algebra Examples

$x = 3 {(y + 4)}^{2} - 9$

Step 1

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

$a = 3$

$h = - 9$

$k = - 4$

Step 2

Since the value of $a$ is positive, the parabola opens right.

Opens Right

Step 3

Find the vertex $(h, k)$ .

$(- 9, - 4)$

Step 4

Find $p$ , the distance from the vertex to the focus.

Tap for more steps...

Step 4.1

Find the distance from the vertex to a focus of the parabola by using the following formula.

$\frac{1}{4 a}$

Step 4.2

Substitute the value of $a$ into the formula.

$\frac{1}{4 \cdot 3}$

Step 4.3

Multiply $4$ by $3$ .

$\frac{1}{12}$

Step 5

Find the focus.

Tap for more steps...

Step 5.1

The focus of a parabola can be found by adding $p$ to the x-coordinate $h$ if the parabola opens left or right.

$(h + p, k)$

Step 5.2

Substitute the known values of $h$ , $p$ , and $k$ into the formula and simplify.

$(- \frac{107}{12}, - 4)$

Step 6

Find the axis of symmetry by finding the line that passes through the vertex and the focus.

$y = - 4$

Step 7