a)
From the graph, the coefficient of a, b, and c are:
a = -15.19
b = -1.39
c = 5.24
[tex]\begin{gathered} \text{The quadratic model is} \\ h=-15.19t^2\text{ - 1.39t + 5.24} \end{gathered}[/tex]b)
To find the height after 0.30 seconds, you will substitute t = 0.30
[tex]\begin{gathered} h\text{ = -15.19 }\times0.3^2\text{ - 1.39 }\times\text{ 0.3 + 5.24} \\ h\text{ = -1.3671 - 0.417 + 5.24} \\ h\text{ = 3.4559} \\ h\text{ = 3.46 feet} \end{gathered}[/tex]c)
To find the height after 0.52 seconds, you will substitute t = 0.52
[tex]\begin{gathered} h\text{ = -15.19 }\times0.52^2\text{ - 1.39 }\times\text{ 0.52 + 5.24} \\ h\text{ = -4.11 - 0.723 + 5.24} \\ \text{h = 0.417} \end{gathered}[/tex]d)
0.30 seconds is more reliable.
e)
[tex]\begin{gathered} h=1foot_{} \\ h=-15.19t^2\text{ }-\text{ 1.39t + 5.24} \\ 1=-15.19t^2\text{ - 1.39t + 5.24} \\ 15.19t^2\text{ + 1.39t + 1 - 5.24 = 0} \\ 15.19t^2\text{ + 1.39t - 4.24 = 0} \end{gathered}[/tex]t = 0.48455
Final answer
t = 0.48 seconds
