Question

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function and rank the functions based on their axis of symmetry (from smallest to largest).

Answer 1

@superhelp101
@tom982

Answer 2

@prettylady01, I'll happily help you with this but I'm not just answering your questions for you. Give it a try and I'll help you if you get stuck - feel free to ask any questions if you get stuck!

Answer 3

@tom982 I graphed the first two equations. So I got a point for both of the vertex. What do I do next?

Answer 4

I think the answer for f(x) is -4 and the answer for g(x) is 4.

Answer 5

The equation f(x) can be found by setting the expression inside the parentheses equal to zero. So you would have x+4=0, and when you solve that you get -4 so the axis of symmetry for f(x)=-4. For g(x) you have to use the equation -b/2a. So substitute -16 in for b and 2 in for a. So you would have -(-16)/2(2). Then the two negatives cancel and 2(2) is 4 so you would have 16/4. You solve that and you would get 4 for the axis of symmetry for g(x). h(x) is graphed so you have to look at where is crosses the x-axis and that is 1. So the axis of symmetry for h(x) is 1. From smallest to largest it would go f(x), h(x), then g(x).

Answer 6

Exactly! Great job working this out by yourself - it wasn't too hard was it? To find the vertex of a quadratic, you can see it quite easily when you express the equation in completed square format (like f(x)). You were quick to spot f(x) turns at x=-4 (-4,1). If we write g(x) in the same format we get:

g(x)=2(x-4)^2-17

And hence the vertex is at x=4 (4,-17).

You're also spot on about h(x).

Good work :)