Question 1200121
You can start with {{{x=ay^2+by+c}}}, but look at the given points, too.  Two of them have x coordinate of  -4.  y value for the symmetry axis is for {{{(10+(-6))/2=2}}}.
One of the given points is also the vertex, based on this result.



Use each point to make separate equations.

{{{system(a*2^2+2b+c=4,a*10^2+10b+c=-4,a*(-6)^2+(-6)b+c=-4)}}}


{{{system(4a+2b+c=4,100a+10b+c=-4,36a-6b+c=-4)}}}

Solve the system for a, b, c.


You might try an online tool,  https://www.emathhelp.net/calculators/linear-algebra/gauss-jordan-elimination-calculator/