Respuesta :
the points represent a parabola
the equation is
[tex]y=ax^2+bx+c[/tex]we need the first three points
in this case, I will use
(1,2) (2,5) and (3,10)
for the point (1,2)
[tex]2=a+b+c[/tex]for the point (2,5)
[tex]\begin{gathered} 5=a(2)^2+b(2)+c \\ 5=4a+2b+c \end{gathered}[/tex]for the point (3,10)
[tex]\begin{gathered} 10=a(3)^2+b(3)+c \\ 10=9a+3b+c \end{gathered}[/tex]we have a system of three equations and three variables
[tex]\begin{gathered} 2=a+b+c \\ 5=4a+2b+c \\ 10=9a+3b+c \end{gathered}[/tex]solving the system equation we obtain the values of a,b and c
[tex]\begin{gathered} a=1 \\ b=0 \\ c=1 \end{gathered}[/tex]the equation is
[tex]y=x^2+1[/tex]
