Sketched below is the parabola f, with equation f(x) = -x2 + 4x -3 and a hyperbola g. with the equation (x-p)(y + t) = 3. B, the turning point of f, lies at the point of intersection of the asymptotes of g. A(-1;0) is the x-intercept of g.Diagram
  1. 5.1
    Show that the coordinates of B are (2;1)
    (2)
    1. 5.2
      Write down the range of f.
      (1)
      1. 5.3
        For which value(s) of x will g(x) ≥ 0?
        (2)
        1. 5.4
          Determine the equation of the vertical asymptote of the graph of h if h(x) = g(x + 4)
          (1)
          1. 5.5
            Determine the values of p and t.
            (4)
            1. 5.6
              Write down the values of x for which f(x).g`(x) ≥ 0
              (4)
              (14)
              [{"prnt":"5","num":"5.1","answer":""},{"prnt":"5","num":"5.2","answer":""},{"prnt":"5","num":"5.3","answer":""},{"prnt":"5","num":"5.4","answer":""},{"prnt":"5","num":"5.5","answer":""},{"prnt":"5","num":"5.6","answer":""}]

              Answers

                1. 5.1
                2. 5.2
                3. 5.3
                4. 5.4
                5. 5.5
                6. 5.6
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