Edexcel P1 2022 June — Question 5

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicCurve Sketching
TypeFinding quadratic from vertex information

  1. The curve \(C\) has equation \(y = \mathrm { f } ( x )\)
Given that
  • \(\mathrm { f } ( x )\) is a quadratic expression
  • the maximum turning point on \(C\) has coordinates \(( - 2,12 )\)
  • \(C\) cuts the negative \(x\)-axis at - 5
    1. find \(\mathrm { f } ( x )\)
The line \(l _ { 1 }\) has equation \(y = \frac { 4 } { 5 } x\) Given that the line \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\) and passes through \(( - 5,0 )\)
  • find an equation for \(l _ { 2 }\), writing your answer in the form \(y = m x + c\) where \(m\) and \(c\) are constants to be found.
    (3) \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-10_983_712_1126_616} \captionsetup{labelformat=empty} \caption{Figure 2}
    \end{figure} Figure 2 shows a sketch of the curve \(C\) and the lines \(l _ { 1 }\) and \(l _ { 2 }\)
  • Define the region \(R\), shown shaded in Figure 2, using inequalities.