Question

a man throws a ball off the top of a building and records the height of the ball at different times as shown in the table:

Height of the ball

time (s) Height (feet)
0 46
1 63
2 48
3 1

a. Find a quadratic model for the data
b. Use the model to estimate the height of the ball at 2.5 seconds
c. What is the ball's maximum height?

Answer 1

I am totally lost...

Answer 2

\[y=-a(x-h)^2+k\]
(1,63) is a Vertex and also a maximum value
\[y=-a(x-1)^{2}+63\]
(0,46) x=0, y=46
\[46=-a(0-1)^{2}+63\]
\[48=-a+63\]
\[a=63-46=17\]
therefore the equation: \[y=-17(x-1)^{2}+63\]
at time 2.5 seconds you plug x=2.5 in the equation
the maximum value (1,63)

Answer 3

My teacher told me the answers for these but I'm lost as to how to get the anwers. She said the answers were:
a. y= -16x^2 + 33x +46, where x is the number of seconds after release and y is the height in feet.
b. 28.5 feet
c. about 63 feet