• The Same roots
,• The same axis of symmetry
1) If we compare two parabolas from this family, like:
[tex]\begin{gathered} f(x)=-1(x-4)(x-8) \\ g(x)=2(x-4)(x-8) \end{gathered}[/tex]Note that the difference is in the leading coefficient "a".
2) Both parabolas will have the same roots, the same x-intercepts:
[tex]x_1=4,x_2=8[/tex]In addition to this, we can state that both will share the same axis of symmetry:
[tex]\begin{gathered} f(x)=-1(x-4)(x-8) \\ f(x)=\quad -x^2+12x-32_{} \\ h=\frac{-12}{2(-1)}=6 \end{gathered}[/tex]As well as:
[tex]\begin{gathered} g(x)=2(x-4)(x-8) \\ g(x)=2x^2-24x+64 \\ h=\frac{24}{2(2)}=6 \end{gathered}[/tex]Hence, the answer is:
0. Same roots
,1. Same axis of symmetry
