Moderate -0.8 This is a straightforward simultaneous equations question requiring substitution to find intersection points, then sketching both graphs with axis intercepts. The algebra is routine (solving a quadratic), and the sketching requires only standard techniques with no geometric insight. Easier than average A-level content.
5.
A curve \(C\) and a straight line \(L\) have respective equations
$$y = x ^ { 2 } - 4 x - 5 \text { and } y = 2 x - 14$$
a) Find the coordinates of any points of intersection between \(C\) and \(L\).
b) Sketch in the same diagram the graph of \(C\) and the graph of \(L\).
The sketch must include of any points of intersection between the graph of \(C\) and the coordinate axes, and any points of intersection between the graph of \(L\) and the coordinate axes.
5.
A curve $C$ and a straight line $L$ have respective equations
$$y = x ^ { 2 } - 4 x - 5 \text { and } y = 2 x - 14$$
a) Find the coordinates of any points of intersection between $C$ and $L$.\\
b) Sketch in the same diagram the graph of $C$ and the graph of $L$.
The sketch must include of any points of intersection between the graph of $C$ and the coordinate axes, and any points of intersection between the graph of $L$ and the coordinate axes.\\
\hfill \mbox{\textit{SPS SPS SM 2021 Q5 [8]}}