Search over 10,000 free study notes

We can first draw the graph of y = f(x) = x^2 which is a simple graph like this (whiteboard). Now looking at y = f(x) + 3, we can see that this is a translation by the vector [0 3]. Therefore we can tr...

You can do this a couple of ways. The first is by using the quadratic equation shown below. Each letter corresponds to the the coefficient of different powers of x. A is the number in front of x^2 and b i...

1. Read the question carefully to understand what it is asking2) Consider how to approach the question - is there more than one way of getting the answer, are there any things that could trick me out (...

The question is asking us to find gf(x).
When approaching this question, the first thing I tend to look for is what information we have that we can break down. In this case, I can immediately see tha...

The graph has two distinct real roots (x=-4 and x = -2), which we can see by factorising the equation, which gives (x+4)(x+2) = 0. We can then plot the function y = x^2 + 6x + 8, first marking the roots o...