All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c\) is a smooth curve with one turning point. The turning ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(y = f(x)\) where \(f(x) = x^2\) is the same as the ...

Explore our campus, meet lecturers and current students, and learn more about what it's like to study at Manchester. Lay the foundations of a rewarding career with mathematics at its base by ...

Explore our campus, meet lecturers and current students, and learn more about what it's like to study at Manchester. We place social responsibility at the heart of your learning which means you can ...

you know basic definitions and results in graph theory you know matroid theory and discrete optimizing problems and algorithms you know modular arithmetic and its use ...

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know basic definitions and results in graph theory, such as trees and shortest path, bipartite graphs and the Traveling Salesman Problem you know various combinatorial counting problems and algorithms ...