IP2 Class Test (May 2025) Q10 (2024 RGS Y2 CBA1 Q5)

The diagram shows the graph of \(y = x^2 - x - 5\) for \(-3 \le x \le 4\).
Use the graph to answer the following questions. Present your solutions on the next page.

1. Using the above graph,
   1. find the value of \(y\) when \(x = 3\)[1]
   2. write down the coordinates of the turning point,[1]
   3. write down the equation of the line of symmetry,[1]
   4. estimate the solutions of the equation \(x^2 - x - 5 = 0\).[1]
2. A suitable straight line is to be drawn on the same diagram to solve the equation \(x^2 - 3x - 2 = 0\).
   1. State the equation of the straight line to be drawn.[1]
   2. Explain how the straight line in (ii)(a) drawn on the graph can lead to an estimation of the solution(s) to the equation \(x^2 - 3x - 2 = 0\).[1]
   3. Hence solve \(x^2 - 3x - 2 = 0\) graphically.[1]