MATH 32 Study Guide - Midterm Guide: Quadratic Equation, Quadratic Function, Inverse Function
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Midterm 1 solutions (1) suppose that the motion of a ball through the air is described by the equation h(t) = Solution: (a) we need to maximize the quadratic function h, which we can do by nding the vertex of the parabola which is its graph. T2 + 4t + 4 = (t2 4t) + 4. = ((t 2)2 4) + 4. Now we can read o the vertex: (2, 8). This means that at time t = 2, the ball is at height h(t) = 8. So the answer is 8 feet. (b) we need to solve the equation h(t) = 0 for t. using the quadratic equation, t2 + 4t + The solution 2 2 after being thrown when the ball hits the ground), so the answer is 2 + 2. 2 is negative, and we"re looking for a positive answer (the time t.
