Question

How do I find the axis of symmetry of f(x)=3(x-4)²-2

Answer 1

we look at the (x-4)^2 which tells us the axis of symmetry X=4

Answer 2

If you know how the function f(x) = x^2 looks like you can easily find the axis of symmetry for this function.

f(x) = x^2 is a parabola that opens up, touches the origin and has the y-axis as the axis of symmetry.

3(x-4)²-2 is also a parabola that looks like f(x) = x^2, except it has been shifted to the right by 4 units and shifted down by 2 units. So the axis of symmetry is x = 4.

Answer 3

If you take f(x) = x^2 and change it to (x - 4)^2 then you have shifted it to the right by 4 units. When you subtract 2 from it, it becomes (x - 4)^2 -2 and you have shifted the parabola down by 2 units.