11. Diane was standing on a roof and threw a weight with a string attached to a nearby roof. The height of the weight above the ground is modelled by the function: h(t) = -5t squared + 10t + 18 where h(t) is height in metres and t is the time in seconds after the throw. [4 marks] a) Write the function in vertex form. b) What is the maximum height of the weight? c) After how many seconds does the weight reach the ground? Round your answer to the nearest tenth. Please help me with this question, I can't figure it out! Thanks so much!
a) to find the vertex, you must get the axis of symmetry (x=-b/2a). the b term is 10 but add a negative and put it over the a term that is -5 then multiply it by 2. Therefore, the axis of symmetry is 1. Now, we plug in 1 into the equation. Then, you have h(1) = -5(1)^2 + 10(1) + 18. The product is 23. The vertex is (1,23). b) In part a we solved for h (the height) when we substituted 1 for t and got 23. Therefore, 23 meters is the maximum height of the weight. c) For this we are going to have to solve the equation. There are many methods but I would use quadratic formula because it works every time though it does require more work than most methods. You will get 2 answers but we use the positive answer because there are no negative seconds. The answer is 3.1 seconds.
factoring out -5, then completing the square and simplify the result. h(t) = -5(t-1)^2 -13 dh/dt = -10(t-1) max at t=1