[tex]y=ax^2+bx+c \\ \\
(0,3) \\
3=a \times 0^2+b \times 0 + c \\
3=c \\ \\
\hbox{so the equation is:} \\ y=ax^2+bx+3 \\ \\
(-1,-2) \\
-2=a \times (-1)^2+b \times (-1) + 3 \\
-2=a-b+3 \\
-2-3=a-b \\
-5=a-b[/tex]
[tex](-2,-5) \\
-5=a \times (-2)^2+b \times (-2) + 3 \\
-5=4a-2b+3 \\
-5-3=4a-2b \\
-8=4a-2b \\ \\
\hbox{solve the system of equations:} \\
-5=a-b \ \ \ |\times (-2) \\
-8=4a-2b \\ \\
10=-2a+2b \\
\underline{-8=4a-2b \ \ } \\
10-8=4a-2a \\
2=2a \\
\frac{2}{2}=a \\
a=1 \\ \\
-5=a-b \\
-5=1-b \\
-5-1=-b \\
-6=-b \\
b=6 \\ \\
\boxed{y=x^2+6x+3}[/tex]
