Question 4
A2
The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the graph
of g. The parabola has x-intercepts-2 and 6, and y-intercept 6. Its turning point is C. The circle has
its centre at the origin and it passes through the point A, which has coordinates (-2,0). At point B
both the circle and the straight line cut the x-axis. The straight line has y-intercept 1.
4.1 What are the coordinates of B?
4.2 What is the equation of g?

4.3 Write down the equation of the line that is perpendicular to the graph of g and passes through
B.
4.4 Find the equation that defines f.
4.5 Show that C has coordinates (2:8).
4.6 (a) What is the distance between A and C'?
(b) Find the midpoint D of AC.
(c) Write down the equation of the circle that has AC as diameter.


4.7 Find the maximum vertical distance between the graphs of ƒ and g on the interval x € [0; 6].
Hint: First find an expression which defines this vertical distance.
4.8 Use the graphs of ƒ and g (not calculations) to solve

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