Methods Cas units 3 and 4

[tolga]

 

[superflya]

i dont think either of your possibilities are correct,
ur given the turning point so equation of ur parabola can be written as y= (x-z)^2 -8
then u sub in either the x or y intercepts that ur given and u shood be able to find z
got it?

[tolga]

the book has those answers and do u know if we could solve the questions by using simultaneous equations.

[stonecold]

I got z=5  WRONG!

What book is this?  And yeah you need to simultaneous solve.

[stonecold]

I got it.  Solution:




Sub in (0,10) and (5,0) and simultaneous solve:
                    -[1]
                    -[2]

a=2 when z=3   or   a= when z=15

Hence there are two possible answers and both are correct.  To get full marks for this question, you would need to state both answers.

[tolga]

yeah i get what you did but how can you simulataneoulsy solve the question when there (x-z) and (-z) and the rest

[stonecold]

There are two variables, a and z.  There are also two equations containing each of the variables.  When you have the same number of equations as unknown variables, a solution can be found.

You are also posting in the wrong place.  Post your questions on the Mathematics board.

[tolga]

yeah your right but ive tried every way and simply cant get the answer right

[tolga]

if you could just show the full working out please

[brightsky]

I got it.  Solution:




Sub in (0,10) and (5,0) and simultaneous solve:
                    -[1]
                    -[2]

a=2 when z=3   or   a= when z=15

Hence there are two possible answers and both are correct.  To get full marks for this question, you would need to state both answers.

Can you show your full workings out here? I'm interested.

Ahh got it....
    [1]
   [2]

From [1].


         [3]

From [2].

   [4]

Substitute [3] into [4],




And then use the quadratic formula to solve. You should get, as stonecold said, two answers: z=3 and z = 15. They are both correct. (Gee...life without CAS calculators is a tough one....:p)

[stonecold]

Just use a CAS calculator to solve.  I doubt you would ever have to solve a question of this difficulty manually.

Haha I know brightsky!

Edit: I got to the same point, but had no idea how to get the "z"s up the top so I can use the quadratic formula.

[brightsky]

Re: tolga.

Without using the quadratic formula, you can just try solving it via factorization:






Hence, z = 15 or z = 3.

[tolga]

thanks alot

[stonecold]

Just use a CAS calculator to solve.  I doubt you would ever have to solve a question of this difficulty manually.

Haha I know brightsky!

Edit: I got to the same point, but had no idea how to get the "z"s up the top so I can use the quadratic formula.

Hehehe, I used my trusty TI-Nspire for the quadratic equation. No idea how to do that either. :p

Hehe same...ti-nspire ily!