Find the Axis of Symmetry y=1/3(x-5)^2-2

$y = \frac{1}{3} {(x - 5)}^{2} - 2$

Step 1

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

$a = \frac{1}{3}$

$h = 5$

$k = - 2$

Step 2

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

Opens Up

Step 3

Find the vertex $(h, k)$ .

$(5, - 2)$

Step 4

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

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

$\frac{1}{4 a}$

Substitute the value of $a$ into the formula.

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

Simplify.

Combine $4$ and $\frac{1}{3}$ .

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

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{3}{4})$

Multiply $\frac{3}{4}$ by $1$ .

$\frac{3}{4}$

Step 5

Find the focus.

The focus of a parabola can be found by adding $p$ to the y-coordinate $k$ if the parabola opens up or down.

$(h, k + p)$

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

$(5, - \frac{5}{4})$

Step 6

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

$x = 5$

Step 7