Equations with a parameter
A parameter is a number that is not given but fixed. Look at the graph and split into cases: for which a are there roots, and how many?
- Russia: grade 10
Guide
A parameter is a letter such as a standing for a fixed but unknown number. Solve the equation for each allowed value of a: the answer often splits into cases.
Two methods: split cases (for ax = b treat a = 0 and a ≠ 0 apart; for a quadratic look at the discriminant), or draw y = f(x) and the horizontal line y = a: the number of common points is the number of roots.
This is an advanced topic. Move the slider; in the last task type your answer.