snowflake Your answer wouldn't be considered correct, if the coefficient of x2 were 5 ie y = 1 / (5x2) then it'd be correct since that would be a dilation from the y-axis

      Billzene

      Ohh ok but how do we whether to work out it’s dilation from the X or Y axis if it doesn’t say in the question?

          snowflake by recognition of the form y = a/(1/b(x-h))n + k

          a = dilation factor from x axis
          b = dilation factor from y axis
          h = translation in +ve direction of x axis
          n = power
          k = translation in the positive direction of y axis

          This is similar to turning point form of parabolas

              5 days later

              find values of a and b such that a(x+2)+b(x+3)=18x+8 for all values of x
              if someone could help that would be great

                chemistry1111 Expand then factorising LHS gives (a+b)x + (2a + 3b) = 18x + 8 --> by comparing coefficients, you obtain a+b = 18 and 2a+3b =8, solve simultaneously for a and b, giving a=46 and b=-28

                  thank you so much that makes sense

                  also this question
                  For the polynomial P(x)=(a+1)x3 + (b-7)x2 +c+5, find values for a,b and c if P(x) has a degree 2, a leading coefficient of 3 and the constant term is -1

                  when factorizing polynomials in methods unit 3/4, what method do most people use vcaa prefer, long division or equating coefficients

                  9 days later

                  Do we need to buy the new Methods 3/4 book for the new study design (2023)?
                  I feel like the textbook questions are the same...

                  4 days later

                  PizzaMaster
                  Howdy, I did QCE Methods, so if I mess this up, I’m really sorry.

                  https://ibb.co/m0Q1xdV

                  For b) may I know what the answers are? I may be able to work backwards 🙂

                  I didn’t do d) because I wasn’t that confident in doing the question.

                  Hope this helps,
                  -jinx_58

                    20 days later

                    Hi jinx_58,

                    Thank you so much for solving!
                    The answer to part b is Domain = [0, 6]; Range = [0, 9/2]
                    The answer to part c is 9/2

                    The graph of y = 5/x -6 is reflected in the x-axis and
                    then in the y-axis. The equation of the final image is:

                    could someone help with this question

                      chemistry1111

                      1. reflected in the x-axis
                      2. reflected in the y-axis

                      **I'm not quite sure if y = (5/x) -6 or if it's y = 5/(x-6) so I'll show the working for both

                      let f[x] = (5/x) -6

                      1. x reflection: -f[x] = f1[x] = -[ (5/x) - 6 ] = -( 5/x ) + 6

                      2. y reflection: f1[-x] = f2[x] = -(5/ [-x] ) +6 = -(5/ x ) +6

                      let g[x] = 5/(x-6)

                      1. x reflection: -g[x] = f1[x] = -[ 5/(x-6) ] = -5/(x-6)

                      1. y reflection: g1[-x] = f2[x] = -5/( [-x] - 6) = -5/( -x - 6)

                      hope that helps!

                        Hi everyone,

                        Is (2x-1) the same as (x-1/2)
                        I mean they both give x= 1/2
                        But let's say if we had to factorise 12x3 + 20x2 − x − 6
                        and we get (2x-1)(2x+3)(3x+2)

                        Can I also write this as:
                        (x-1/2)(2x+3)(3x+2)?

                        ALSO can some please help and find the roots of this: 12x3 + 20x2 − x − 6
                        using rational root theorem

                        much appreciated!!!

                          PizzaMaster
                          good question! to answer your first one, (2x-1) = 2 (x-1/2). they're not the same but the same x value will make both of them equal (0). I'm not home rn so I'll reply to the second one when I have access to my iPad.

                          EDIT
                          I think it's easier if you watch a video, here's a good one I found (watching 0:00-2:40 should be enough): https://www.youtube.com/watch?v=4XytYH35AP0

                            So I can write (2x-1)(2x+3)(3x+2) as 2(x-1/2)(2x+3)(3x+2) NOT (x-1/2)(2x+3)(3x+2)
                            Great, thanks crumblycupcakes!

                            With rational root theorem, I find that it is super time consuming... after we find the possible roots, is there a shortcut to know which ones to try first?
                            For example with 12x3 + 20x2 − x − 6:
                            the possible roots are +- [1/2, 1/3, 1/4, 1/6, 1/12, 2/3, 3/4, 3/2]
                            That is a lot! Is there a way to know which one we can try first?

                            Also does simplifying work?
                            for example with 12x3 + 20x2 − x − 6, we do like factors of 6/ factors of 12. Can we do factors of 1/ factors of 2 (since 6/12 = 1/2?)