Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t 2 + 40t, where h represents the height of the ball above the ground and t represents the time in seconds. The maximum value achieved by the function is represented by the vertex. Use factoring to answer the following:How many seconds does it take the ball to reach its highest point?What ordered pair represents the highest point that the ball reaches as it travels through the air?Hint: because parabolas are symmetric, the vertex of a parabola is halfway between the zeroes of the quadratic.
Accepted Solution
A:
Answer:Time to highest point: 5/2, or 2.5 secondsOrdered pair: (5/2, 50)Step-by-step explanation:Find the vertex of h(t). This will be the highest point of the ballFind the x coordinate of the vertex with the formula: x = -b/(2a)x = -40/[2(-8)] = -40/-16 = 5/2to find the y value, plug 5/2 into the equation and solveh(5/2) = -8(5/2)² + 40(5/2) h(5/2) = -8(25/4) + 200/2 h(5/2) = -200/4 + 100 h(5/2) = 50So the ball reached a maximum height of 50 feet