2023 May TZ2 P1 Q7

The following diagram shows part of the graph of a quadratic function \(f\).
The vertex of the parabola is \( (-2, -5) \) and the \(y\)-intercept is at point \(\mathrm{P}\).

1. Write down the equation of the axis of symmetry

   [1]

The function can be written in the form \(f(x) = \frac{1}{4}(x - h)^2 +k\), where \(h, k \in \mathbb{Z}\).

2. Write down the values of \(h\) and \(k\).

   [2]

3. Find the \(y\)-coordinate of \(\mathrm{P}\).

   [2]

In the following diagram, the line \(L\) is normal to the graph of \(f\) at point \(\mathrm{P}\).

4. Find the equation of the line \(L\), in the form \(y = ax + b\).

   [4]

The line \(L\) intersects the graph of \(f\) at a second point, \(\mathrm{Q}\), as shown above.

5. Calculate the distance between \(\mathrm{P}\) and \(\mathrm{Q}\).

   [8]