Answer
See below
Work Step by Step
The standard form of the equation is: $y=ax^2+bx+c$
Given three points: $(-0.5,-1)\\(2,8)\\(11,25)$
Substitute: $-1=a(-0.5)^2+b(-0.5)+c\\8=a(2)^2+b(2)+c\\25=a(11)^2+b(11)+c$
We have the system: $0.25a-0.5b+c=-1\\4a+2b+c=8\\121a+11b+c=11$
Multiply the second equation by $-1$ and add to the third equation:
$117a+9b=17$
Multiply the first equation by $4$. Multiply the second equation by $-4$ and add it to the first one:
$-15a-10b=-36$
We have the new system:
$-15a-10b=-36\\
4a+2b+c=8\\
117a+9b=17$
Multiply the third equation by $\frac{10}{9}$ and add to the first:
$-15a-10b+\frac{10}{9}(117a+9b)=-36+\frac{10}{9}.17\\
\rightarrow 115a=-\frac{154}{9}\\
\rightarrow a=-\frac{154}{1035}$
Substitute: $-15(-\frac{154}{1035})-10b=-36\\
\rightarrow b=\frac{3957}{1035}$
Find $c$: $-\frac{154}{1035}-2(\frac{3957}{1035})+4c=-4\\
\rightarrow c=\frac{982}{1035}$
Hence, $a=-\frac{154}{1035}\\b=\frac{3957}{1035}\\c=\frac{982}{1035}$
Substitute back to the initial equation: $y=-\frac{154}{1035}x^2+\frac{3957}{1035}x+\frac{982}{1035}$
