Answer:
[tex]-x^2+5x[/tex]
Step-by-step explanation:
Let the quadratic be [tex]ax^2+bx+c[/tex]. Therefore, if you plug in the first point,
[tex]a(0)^2+b(0)+c=0\\c=0[/tex]
and if you plug in the 2 other points,
[tex]a-b=-6\\4a+2b=6[/tex]
Multiply the first equation by 2:
[tex]2a-2b=-12[/tex]
and add it up to the second equation:
[tex]6a=-6\\a=-1[/tex]
Lastly, plug in a for the first equation:
[tex]-1-b=-6\\b=5[/tex]
Therefore, the final quadratic is [tex]\boxed{-x^2+5x}[/tex]
