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 − 2x
y = −2x2 + 4x − 3

Answer 1

How would I do this?

Answer 2

Well the direction will be opening upwards as \(x^2\) term is positive

Answer 3

what equation forms for parabolas do you know?

Answer 4

you could graph them both...

Answer 5

Case 1 : \(y= ax^2 + bx + c\) when \(a>0\) , the parabola is opening upwards
Case 2 : \(y = ax^2 + bx + c\) when \(a<0\) , the parabola is opening downwards.

Answer 6

Ok, thanks . . .

Answer 7

Differentiate : \(y = x^2-4x\) , what do you get?

Answer 8

ummmm . . . y = (x-4) x ?

Answer 9

Do you know differentiation?

Answer 10

apparently not

Answer 11

it will come later

Answer 12

Ok . . . I am officially confused.

Answer 13

Hmn. Let us do it with other method then!

Answer 14

Ok fine by me . . .

Answer 15

Well is it \(x^2-2x\) or \(x^2-4x\) ?

Answer 16

The 1st one why wouldn't it be?

Answer 17

Hmn just asking as if it was \(x^2-4x\) then it may have been little bit easier for me.

Answer 18

The is 2 grades above me . . .

Answer 19

ok1 no problem .. Let us do it as \(x^2-2x + 2 - 2 = y\)

is it fine for you?

Answer 20

Yes

Answer 21

Ok fine, forget it. I have to think more.

Answer 22

Confused . . .

Answer 23

Wait for 1 min. more frank

Answer 24

Ok

Answer 25

Actually the problem I am having is that I have to complete the square of \(x^2-2x\) ,,,

Answer 26

Ok got it.

Answer 27

\(x^2- 2x +1-1 = y\) Fine again?

Answer 28

Yes

Answer 29

Now Can I write \(x^2-2x+1 = x^2 - x - x +1 = x(x-1) - (x-1) = (x-1)(x-1)\) ?

Answer 30

Or \(x^2-2x +1 = (x-1)^2\) ?

Answer 31

Bleg . . . I don't realy get any of this . . .

Answer 32

hmn : what is (a-b)^2?

Answer 33

(a-b)(a-b)?

Answer 34

Expand that frank.

Answer 35

If you have \[(a-b)^{2} \] wouldn't you just be multiplying them by themselves?

Answer 36

\((a-b)(a-b)\) = \(a(a) - a(b) -b(a) -b(-b)\)
right?

Answer 37

I think so . . .

Answer 38

now try to simplify it:

\(a(a) - a(b) - b(a) -b(-b)\)