Find a parametrization for the curve...

The left half of the parabola y=x^2+2x

Question

Find a parametrization for the curve...

The left half of the parabola y=x^2+2x

tkhunny · Answer

You will have to know where the middle is.  Where?

anonymous · Answer

that's the only information given

tkhunny · Answer

It is enough information to solve the problem.

Now that we have that out of the way, you will have to know where the middle is.  Where?

anonymous · Answer

I have no clue, which is why I need help

anonymous · Answer

can you please just help me, step by step? I really wanna understand this

tkhunny · Answer

I am trying.  You don't seem to want to do anything.  Can you find the center of the parabola or not?  If you are in calculus, learning to parameterize curves, you should have a decent background in conic sections.  Now is the time to prove you took the prerequisites.

Find the vertex of that parabola!

anonymous · Answer

I haven't taken calculus yet, it is a summer packet on prerequisites and I don't understand any of it, but I'll try.

tkhunny · Answer

Hint: Factor and find the zeros.  You will find the vertex on the center line exactly between those zeros.

anonymous · Answer

-2,8?

tkhunny · Answer

What is that?  You must show your work and explain your intent.  Just dumping out data almost never is helpful.

anonymous · Answer

$$x(x+2), x=0, x+2=0    $$

anonymous · Answer

$$x=-2, y=(-2)^2+2(-2), y=8$$

tkhunny · Answer

It was supposed to be a zero.  Why didn't it come out (-2,0)?

anonymous · Answer

sorry it is -2,0 I kept putting 8

tkhunny · Answer

Okay, now we know the zeros.  (0,0) and (-2,0)

This gives us the center line x = -1

Evaluate at x = -1 and you will find the vertex.

Are we ringing any bells or is this all new?

anonymous · Answer

ugh just forget it, I don't get it

anonymous · Answer

If you're having trouble following @tkhunny's suggestion: Another way of finding the vertex is by writing the parabola in vertex form,
$$y=a(x-h)^2+k,~\text{where the vertex is }(h,k)$$
Do you know how to do that?

tkhunny · Answer

This is the point of a pre-test - to see where you are.  It appears to me that you will need a little more background in analytic geometry before proceeding to the calculus.

Good luck - wherever you land.

anonymous · Answer

@SithsAndGiggles no I don't, but thanks for trying to help, i'll just skip it