Part 1
The gradient of the line is [tex]\frac{11-1}{-3-2}=-2[/tex], so the equation is [tex]y=-2x+5[/tex].
This means the system is
[tex]y=-2x+5\\\\y=ax^2 +b[/tex]
Part 2
Substituting in the coordinates (-3,11) and (2,1) into the equation of the parabola,
[tex]11=9a+b\\\\1=4a+b[/tex]
Subtracting the equations, we get 10=5a, and thus a = 2
Substituting a = 2 back into the system, we get b = -7
Part 3
The equation of the parabola is [tex]y=2x^2 - 7[/tex], and the turning point is at [tex]x=0[/tex]. Therefore, the value of y is -7
