Melody

Yes, we teachers Love to make children suffer...   . 

I think   c

NO Hayley didn't ruin it.

She should always ask when she does not understand :)

Thanks guest,

You are welcome to put your 2 cents in :))

All the praise has gone to my head and now it is very swollen so I do not know if it will fit through doorways anymore.  ://   

Thank you Hayley and guest for your glowing refernces BUT how am i going to fit my head through any door now????

Hi Alan :))

Graph the function: Y=x^2+4x+3..

Vertex:

Axis of Symmetry:

Domain:

Range:

\(y=x^2+4x+3\)

This is a parabola because it is a polynomial of degree 2  (The highest power of x is 2)

There is an invisable +1 in front of the x^2    (1 is the leading coefficient)

Since the leading coefficient is positive the parabola is concave up.

\(y=x^2+4x+3\\ y=(x+3)(x+1)\\ \)

The roots of the parabola are where y=0

y will equal zero when  x+3=0  and when  x+1=0

roots are x = -3  and x = -1

The axis of symmetry will be half way between the roots

x=(-3+-1)/2 = -4/2 = -2

Axis of symmetry is   x = -2

When x=-2    y=2^2-4*2+3 = 4 -8 +3 = -1   So the vertex is (-2, -1)

 Domain:  \(x \in Z\)  (x can be anything)

Range:      \(y\ge-1\)

The vertex is where y=-1 so this is the lowest value that y can take.

and here is the graph

Tues 15/12/15     Wed 16/12/15

1)  Please do Not post on unpleasant threads.

     https://web2.0calc.com/questions/please-do-not-make-unpleasant-threads-longer

2)  Probability and fun     Melody Nauseated, Queen Guinevere and MorganTud

     https://web2.0calc.com/questions/statistics-probability-question

3)  Understanding Parabolas    Thanks Alan and Melody.

     http://web2.0calc.com/questions/please-and-thank-you-lt-3

4)  How far is it ?

     https://web2.0calc.com/questions/where-is-my-mistake

5)  Percentage algebra question.     Thanks Heureka

     https://web2.0calc.com/questions/percentage-algebra-question

6)  Space travel, lightyears and revolutions    Thanks Heureka

     https://web2.0calc.com/questions/the-starships-enterprise-and-intrepid-after-refits-are-undergoing-flight-tests

7)  Multiple roots equation    Melody

     https://web2.0calc.com/questions/see-if-you-can-solve-this-tough-one-show-work

8)  Mass velocity and kinetic energy    Thanks Heureka

     https://web2.0calc.com/questions/physics-help_3

9)  Good Simultaneous Equation Question   Thanks Heureka and guest

     https://web2.0calc.com/questions/algebra-word-problem-4

idk why either :/      (But thanks Hayley)

I put the wrong date :(  oh well too bad.

I fixed it in the post but the address is the 15th instead of the 14th  ://

@@ What is Happening?  [Wrap4]   Mon 14/12/15   Sydney, Australia Time 12:25 am  (really Tuesday)    ♪ ♫

Good evening from Australia,

We have had some great answers delivered by cdromdj, Complex, Badinage, Hayley1, Heureka and jc.     Thank you.   

Technical Issues:

How can you post a picture when the picture upload on the forum is not working properly ?

Thanks very much Alan for these instructions.