First of all, we have to find Parabola 2. The general formula is
[tex] g(x) = ax^{2} +bx+c [/tex].
It is given that the leading coefficient is 1, then a=1. Putting 4 and -2 into the formula, we have to solve the following system of equations:
[tex] \left \{ {{16+4b+c=0} \atop {4-2b+c=0}} \right. [/tex]
Solving it, we find that b=-2 and c=-8
Parabola 2 is given with
[tex] g(x)=x^{2} -2x-8 [/tex]
Both functions have a minimum because the parabolas located upwardly. The minimum of Parabola 1 is located below the minimum of Parabola 2. You can observe this result in the attached picture, as well. Parabola 1 is given with blue line.
