Question

what type of function linear exponential or quadratic best models the date in each table

Answer 1

The general quadratic equation is,

$y=ax^2+bx+c$

For x = 0, y = 0.

$\begin{gathered} 5=a(0)^2+b(0)+c \\ c=5 \end{gathered}$

For x = 1, y = 6,

$\begin{gathered} 6=a(1)^2+b(1)+5 \\ a+b=1 \\ b=1-a \end{gathered}$

For x = 2, y = 9,

$\begin{gathered} 9=a(2)^2+b(2)+5 \\ 4a+2(1-a)=4 \\ 2a=2 \\ a=1 \end{gathered}$

Determine the value of b.

$\begin{gathered} b=1-1 \\ =0 \end{gathered}$

The relation between varaible is,

$y=x^2+5$

So function is quadatic, which models the data in the table.