A frog jumps and takes 2 seconds to land. The path of the frog’s flight is best modeled by the graph of f(x) = -x2 + 2x. What is the maximum height of the jump?
The flight path of a frog is best modeled by the graph of f(x) = -x2 + 2x and it can be used to determine the maximum height of its jump. The equation for this graph describes a parabola, which is symmetrical around its vertex. To find the maximum height, we must first locate the vertex of this parabola. We can do this by taking the derivative of f(x), which gives us -2x + 2; setting it equal to zero in order to find where its slope is 0 will result in x=1. This means that at x=1, we have found our vertex point with coordinates (1, 1).
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