Question

1 quick math help question

Answer 1

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

I know the answer for a is y=-16x^2+33x+46

Answer 2

let the time be \(\large t\)
hence \(\Large f(t)=ax^2+bx+c\)
\(\large\tt \begin{align} \color{black}{ f(t)=ax^2+bx+c\\~\\
f(0)=46\\~\\
f(t)=ax^2+bx+c\\~\\
f(0)=a(0)^2+b(0)+c\\~\\
46=c\\~\\
c=46------\color{red}{ 1}\\~\\
f(1)=63\\~\\
f(1)=a(1)^2+b(1)+c\\~\\
6=a+b+c\\~\\
a+b+c=6------\color{red}{ 2}\\~\\
f(2)=48\\~\\
f(2)=a(2)^2+b(2)+c\\~\\
48=4a+2b+c------\color{red}{ 3}\\~\\\\~\\
\\~\\}\end{align}\)

Answer 3

from eqn 1 ,2 and 3 u have to find
\(\Large a\) and \(\Large b\) , we have found \(\Large c\)

then put the value of \(\Large a\) , \(\Large b\) and \(\Large c\)

in \(\Large f(t)=ax^2+bx+c \\
\implies \Large y=ax^2+bx+c \\
\)

Answer 4

* correction a+b+c=63

Answer 5

Thank you so much! That helped a bunch!

Answer 6

oh welcome