Question: Advanced maths graph solutions 1 [30 marks] This question is about finding the number of solutions to equations, without necessarily finding what those solutions are.

Advanced maths graph solutions

1 [30 marks] This question is about finding the number of solutions to equations, without necessarily finding what those solutions are. a i Sketch the graph y = x2 - 2x + 1. ii Add the line y = 3x to your sketch. How many solutions are there to the equation 12 - 2x + 1 =3x? iii Use a discriminant method to find the values of a for which to the equation x2 - 2x + 1 = ax has zero, one or two distinct solutions. iv In the two situations in part iii where there is only one solution, sketch the graphs of y=x - 2x + 1 and y = ax. What is the geometric relationship between the two graphs in each sketch? [9]

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