Precalculus Examples

$y = 8 {(x - 10)}^{2} - 16$

Step 1

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

$a = 8$

$h = 10$

$k = - 16$

Step 2

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

Opens Up

Step 3

Find the vertex $(h, k)$ .

$(10, - 16)$

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.

$\frac{1}{4 \cdot 8}$

Step 4.3

Multiply $4$ by $8$ .

$\frac{1}{32}$

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 y-coordinate $k$ if the parabola opens up or down.

$(h, k + p)$

Step 5.2

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

$(10, - \frac{511}{32})$

Step 6

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

$x = 10$

Step 7