Functions

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

The \(x\)-intercepts are at \( (-4,0)\) 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]

2. Find another expression for \(f(x)\) in the form \(f(x) = -10(x - h)^2 + k\).

   [4]

3. Show that \(f(x)\) can also be written in the form \(f(x) = 240 + 20x - 10x^2\).

   [2]

A particle moves along a straight line so that its velocity, \(\mathrm{v}\) m s\(^{-1}\), at time \(t\) seconds is given by \(\mathrm{v} = 240 + 20t - 10t^2\), for \(0 \leq t \leq6\).

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.

      [7]