Functions

The following diagram shows part of the graph of a quadratic function \(f\).

The \(x\)-intercepts are \( (-4,0)\) and \( (6,0)\) and the \(y\)-intercept is at \( (0,240)\).

1. Write down \(f(x)\) in the form \(f(x) = -10(x - p)(x - q)\).
2. Find another expression for \(f(x)\) in the form \(f(x) = -10(x - h)^2 +k\).
3. Show that \(f(x)\) can also be written in the form \(f(x) = 240 + 20x -10x^2\).

A particle moves along a straight line so that its velocity, \(\mathrm{v}\) ms\(^{-1}\), at time \(t\) seconds is given by \(\mathrm{v} = 240 + 20t -10t^2\), for \(0 \leq t \leq 6\).

4. 1. Find the value of \(t\) when the speed of the particle is greatest.
   2. Find the acceleration of the particle when its speed is zero,