Algebra Examples

Find the Axis of Symmetry f(x)=2(x-3)^2+5
Step 1
Write as an equation.
Step 2
Use the vertex form, , to determine the values of , , and .
Step 3
Since the value of is positive, the parabola opens up.
Opens Up
Step 4
Find the vertex .
Step 5
Find , the distance from the vertex to the focus.
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Step 5.1
Find the distance from the vertex to a focus of the parabola by using the following formula.
Step 5.2
Substitute the value of into the formula.
Step 5.3
Multiply by .
Step 6
Find the focus.
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Step 6.1
The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Step 6.2
Substitute the known values of , , and into the formula and simplify.
Step 7
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Step 8