Question

7. In some places, a suspension bridge is the only passage over a river. The height of one such bridge, h, in metres, above the riverbed can be modelled by h = 0.005x^2 + 24.
a) How many zeros do you expect the relation to have? Why?
b) If the area was flooded, how high could the water level rise before the bridge was no longer safe to use?

I have answered a) but I don't know how to do b). The book says the answer is 24m if that helps. Any suggestions are appreciated.

Answer 1

Sure. The function is a parabola. Because the coefficient of the x^2 term is positive, it opens upward. that means that it vertex is a minimum point.

You can verify that the vertex is (0,24). That means that at the point x=0, the height of the bridge is 24m. So if the level water rises below 24 m, the bridge is safe to use.