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This is about a topic called graph transformations. It can get quite complicated, but the lucky thing here is that each question can be broken down into steps.

So considering the first question wit...

To answer these questions, students must know the values of cos30 and tan60. If you don't know them off by heart, you can work them out using an equilateral triangle.

cos 30° = adj / hyp =...

We want a solution to ax^2+bx+c=0. Complete the square to get a[(x+b/2a)^2 -(b^2)/(4a^2)]+c=0. Expalding brackets and rearanging gets a(x+b/2a)^2=(b^2)/4a -c. Divide by a to get (x+b/2a)^2= b^2/4a^2 -c/a=...

We start with the definitions of sine and cosine, which are, respectively: sinx = opposite/hypoteneuse and cosx = adjacent/hypoteneuse. We then square the analyzed expressions to get the following: 
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