Please help me with these problems

Liz · 2007-02-06 10:24:20

In problems 22-24 f(x)=7x+4 and g(x)= |x-3|. Evalutate each expression.
23. f(-3)+g(-3)

In Problems 41-45 let f(x)=x^2 +5x -7 and g(x)=x+1

41. Find x so that f(x)=g(x)
43.Find x so that f(x)=g(4x)
45. Find k so that g(k+3)=2g(k)

and the last one, sorry so many but I DONT GET THESE AT ALL!!

In problems 46-49, find the slution set for each equation

47. x(x - 12) = 2(x - 12)

thank you so much, i dont know why i am having so much trouble with these but if someone could help that would fantastic!

luca-deltodesco · 2007-02-06 10:44:02

23.

41.

43.

45.

pi man · 2007-02-06 16:27:38

Plugging 12 in for x:
12(12-12) = 2(12-12)
12(0) = 2(0)
0 = 0

Plugging 2 in for x:
2(2-12) = 2(2-12)
-20 = -20

John E. Franklin · 2007-02-06 16:45:01

On #41, I am quite impressed how you did that factoring without the quadratic formula, which does come out the same I noted. Very interesting luca-d!!! Do you ever need the quadratic formula anymore?? Can you always do that?

John E. Franklin · 2007-02-06 16:52:48

On #43, and I am a little tired, so I might be wrong, but the 35 might be 33, I think.
Thanks for the tip on doing quadratics without the formula!!! Love it.

luca-deltodesco · 2007-02-06 19:17:18

the formula requires that there is an x term in the quadratic: then rather than

you have:

but ofcourse, it makes things much simpler, when a = 1:

but the only thing you actually have to remember, is the 0.5b part in the brackets, then you can just work out the added value from what it should be and what you get when squaring:

for example above:

half of 4 = 2
then , but equation has -8, what do you add to 4 to get -8? -12

Last edited by luca-deltodesco (2007-02-06 19:19:12)

luca-deltodesco · 2007-02-06 19:24:41

actually: i wonder:

lol, never realised the completing the square method was just a rearrangement of the quadratic formula, or perhaps its the other way round, completing the square was discovered first, then quadratic equation derived from it

mathsyperson · 2007-02-06 22:25:47

Yes, the quadratic formula was made by just completing the square for a general equation.
I remember reading the proof for it about 6 years ago and barely understanding.

As for which of the two is better, it's just a matter of personal preference, I think. For the very simple equations, you'd just factorise them instead, so they don't count. I think completing the square is a nicer method, because you're actually using maths rather than just being a robot and plugging into a formula that someone else gave you, but the quadratic formula is good if a, b and c are huge, because no matter how big they are, you can just put it all into a calculator and get the answer easily.

George,Y · 2007-02-07 01:04:13

lol, never realised the completing the square method was just a rearrangement of the quadratic formula, or perhaps its the other way round, completing the square was discovered first, then quadratic equation derived from it
-Yes, sure. Lucky me that our textbook derived this formula naturally.

John E. Franklin · 2007-02-07 04:20:42

Thanks again luca-d for the excellent description of how this works.
Here is an example that I just made up that just plain divides out the "a"
constant to one, since the other side of equation is zero, this is okay.

Last edited by John E. Franklin (2007-02-07 04:27:17)

Math Is Fun Forum

#1 2007-02-06 10:24:20

Please help me with these problems

#2 2007-02-06 10:44:02

Re: Please help me with these problems

#3 2007-02-06 16:27:38

Re: Please help me with these problems

#4 2007-02-06 16:45:01

Re: Please help me with these problems

#5 2007-02-06 16:52:48

Re: Please help me with these problems

#6 2007-02-06 19:17:18

Re: Please help me with these problems

#7 2007-02-06 19:24:41

Re: Please help me with these problems

#8 2007-02-06 22:25:47

Re: Please help me with these problems

#9 2007-02-07 01:04:13

Re: Please help me with these problems

#10 2007-02-07 04:20:42

Re: Please help me with these problems

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