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This is an example of completing the square.If we expand (x - p)^2 + q, we will have x^2 -2px + p + q.Now we can use algebra to work out what p and q are from the following equation. x^2 - 7x + 2 = x^2 -2...

Let the parabola be y=x² and let the family of lines be y=2x+c, in order to study the intersection points we need to consider the second order linear system given by having the two equations ab...

By multipying across and using some trigonometric identities we can turn this in to a much simpler quatratic which can be solved using the quadratic formula. This step can be simplified by using the subst...

To differentiate composite functions, (a function within a function) like in this case we need to use the chain rule. We can see that F(x)=f(g(x)) where we let f(x)= (x^2+1)^2 and g(x)= x^2+1. To use the ...

A radian is the angle in a segment that gives an arc length of 1 radius. This is another way to measure angles instead of degrees. As the circumference of a circle is 2pir, we have 2pi radius...