SOLUTION: The function h(t) = {{{ -16t^2 + 144t + 576 }}} gives the height (in feet) of a rock t seconds after it has been thrown upward. Draw the graph of h. Determine the maximum height

Algebra ->  Functions -> SOLUTION: The function h(t) = {{{ -16t^2 + 144t + 576 }}} gives the height (in feet) of a rock t seconds after it has been thrown upward. Draw the graph of h. Determine the maximum height       Log On


   

Question 906686: The function h(t) = ++-16t%5E2+%2B+144t+%2B+576+ gives the height (in feet) of a rock t seconds after it has been thrown upward. Draw the graph of h. Determine the maximum height of the rock and the time that it takes the rock to reach that maximum height. How do you know that there is a maximum height? Justify your answer.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-16t%5E2+%2B+144t+%2B+576+
this is a parabola that opens downward and its vertex is max point
+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+950%2C-16x%5E2+%2B+144x+%2B+576+%29+
find coordinates of vertex:
t or x-coordinate: t=-b%2F2a => t=-144%2F2%28-16%29=-144%2F-32=4.5
plug it in +h%28t%29+=+-16t%5E2+%2B+144t+%2B+576+ and find h or y-coordinate
+h%284.5%29+=+-16%284.5%29%5E2+%2B+144%2A4.5+%2B+576+
+h%284.5%29+=+-16%2820.25%29+%2B+648+%2B+576+
+h%284.5%29+=+-324+%2B+1224+
+h%284.5%29+=+900+
so, vertex is at (t,h)= ( 4.5 ,900) and the maximum
height of the rock is h=900 and the time that it takes the rock to reach that maximum height is 4.5s