Compare and contrast the two quadratic equations below. In order to receive full credit, use complete sentences to describe the following:

The direction each parabola opens
The vertex of each parabola
y = x2 − 4x
y = −2x2 + 8x − 12

Question

Compare and contrast the two quadratic equations below. In order to receive full credit, use complete sentences to describe the following:

The direction each parabola opens
The vertex of each parabola
y = x2 − 4x
y = −2x2 + 8x − 12

terenzreignz · Answer

So, how do you know the direction a parabola opens?

anonymous · Answer

by the sign in front of the a term

terenzreignz · Answer

so, in what direction do these two parabolas open?
Are they the same direction?

anonymous · Answer

no two different ones up then down

anonymous · Answer

idk how to find the vertex

terenzreignz · Answer

That's right, they're different :D

terenzreignz · Answer

ahh okay :)
Do you know the vertex formula?

anonymous · Answer

nope

terenzreignz · Answer

I could give it to you right away, or do you want to derive some of it yourself?

anonymous · Answer

no

anonymous · Answer

ill try and do it

terenzreignz · Answer

Hmph Oh well

If your parabola is of the form
$$f(x) = ax^{2} + bx + c$$
Then your vertex (h,k) is given by

$$h = \frac{-b}{2a}$$$$k=\frac{4ac-b^{2}}{4a}$$

Work from there :)

anonymous · Answer

My Answer:
y = x^2 − 4x

Well, for this first equation, the direction the parabola opens is upward, and the vertex would be (2, -4). 

y = −2x2 + 8x − 12 

For the second equation, the direction the parabola opens is downward, and the vertex is (2, -4) as well. 

Does this sound okay? Does it make sense, do I have everything correct?

terenzreignz · Answer

That's right :)
So you can do it from here?

anonymous · Answer

yep