Question

The order pairs (1,2), (2,5), (3,10), (4,17), and (5, 26) represents a function. what is a rule that could represent this function?

Answer 1

the points represent a parabola

the equation is

`y=ax^2+bx+c`

we need the first three points

in this case, I will use

(1,2) (2,5) and (3,10)

for the point (1,2)

`2=a+b+c`

for the point (2,5)

`\begin{gathered} 5=a(2)^2+b(2)+c \\ 5=4a+2b+c \end{gathered}`

for the point (3,10)

`\begin{gathered} 10=a(3)^2+b(3)+c \\ 10=9a+3b+c \end{gathered}`

we have a system of three equations and three variables

`\begin{gathered} 2=a+b+c \\ 5=4a+2b+c \\ 10=9a+3b+c \end{gathered}`

solving the system equation we obtain the values of a,b and c

`\begin{gathered} a=1 \\ b=0 \\ c=1 \end{gathered}`

the equation is

`y=x^2+1`