find and label the vertex and the line of symetry
f(x)= 1/2x^2

Question

chaise · Answer

Line of symmetry (x,y) = (0,0)
Vertex (x,y) = (0,0)

anonymous · Answer

I do not think that a x^2 graph has a vertex. The correct answer is there is no vertex.

anonymous · Answer

The direction of the slope does not change at (0,0)

chaise · Answer

The vertix is the turning point. When you draw the graph of x^2 it turns at (0,0). Is this not correct?

anonymous · Answer

No, imagine drawing arrows along the graph. The arrows will always form a counterclockwise spin. At a turning point, these arrows would change the direction of the spin.

anonymous · Answer

Hard to explain without drawing, but you can prove that with the second derivative: At a vertex, the second derivative of x^2 has to be zero. The f''(x) of x^2 equals 2. Which is a constant line and has no point at wich f''(x) equals zero.

chaise · Answer

http://www.wolframalpha.com/input/?i=x^2 The graph is drawn - please explain to me how the turning point is NOT at (0,0)?

anonymous · Answer

I think we are both right and wrong, depends how you define a vertex. I just looked, and you are right, a vertex is at (0,0), but it is not a turning point. A turning point, meaning a point of inflection does not exist in a x^2 graph. So I am sorry, I misunderstood the vertex at first.

anonymous · Answer

I am confused about the translations, some use vertex as a turning point, some just as another word for an extrema.

chaise · Answer

It's okay. I was confused, my maths teacher explain the vertex in a parabola is the turning point. :)

anonymous · Answer

http://www.squarecirclez.com/blog/wp-content/uploads/houseprices_1288A/pointofinflection00.gif just to show what I meant ;)

chaise · Answer

Aaah. okay, thank you :)