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.