A bird flying above the edge of the cliff sees a fish several meters below the surface of the water in a lake bounded by the cliff. The bird makes a dive to catch the fish. The path of the dive follows a parabolic curve given by the function y=x^2 - 12x +32. At the right is a graph of this function. Imagine that the x-axis runs along the surface of the lake and the y-axis runs along the edge of a cliff.
a) How far from the side of the cliff is the fish if it is at the vertex of the curve?
b) How far below the surface of the water does the bird have to dive to catch the fish
c) How far from the side of the cliff will the bit enter and exit the water ( x-intercept)?
d) Approximate the height of the cliff ( y-intercept).
e) If the bird enters the water 4 meters from the side of the cliff and exits at 8 meters from the cliff, write an inequality to represent the region in which the fish can swim safely.