Find the Axis of Symmetry f(x)=2(x-3)^2+5

$f (x) = 2 {(x - 3)}^{2} + 5$

Step 1

Write $f (x) = 2 {(x - 3)}^{2} + 5$ as an equation.

$y = 2 {(x - 3)}^{2} + 5$

Step 2

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

$a = 2$

$h = 3$

$k = 5$

Step 3

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

Opens Up

Step 4

Find the vertex $(h, k)$ .

$(3, 5)$

Step 5

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.

$\frac{1}{4 \cdot 2}$

Multiply $4$ by $2$ .

$\frac{1}{8}$

Step 6

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.

$(3, \frac{41}{8})$

Step 7

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

$x = 3$

Step 8