The addition of the value \(a\) represents a vertical translation in the graph. If \(a\) is positive, the graph translates upwards. If \(a\) is negative, the graph translates downwards.

Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...

It is useful to remember that all lines and curves that slope upwards have a positive gradient ... two points on the tangent to the curve. The following graph shows the car journey from Chelsea ...