Answer:
[tex]-3x^{2}+24x-51[/tex]
Step-by-step explanation:
we have that the form of the parabola's equation is
[tex]ax^{2}+bx+c[/tex]
an also we have
[tex]a(4)^{2}+b(4)+c=-3\\a(5)^{2}+b(5)+c=-6[/tex]
and for the vertex in (4,-3)
[tex]x=-\frac{b}{2a}[/tex]
[tex]4=-\frac{b}{2a}\\b=-8a[/tex] (1)
if we subtract the first equation to the second equation we can obtain a 2x2 system equation
[tex]9a+b=-3\\b=-3-9a[/tex] (2)
and by taking the equations (1) and (2)
[tex]-8a=-3-9a\\a=-3[/tex]
hence, for b we have
[tex]b=-8(a)=-8(-3)=24[/tex]
and to compute c we can use
[tex]a(4)^{2}+b(4)+c=-3\\(-3)(16)+(24)(4)+c=-3\\c=-51[/tex]
Finally we have that the parabola is
[tex]-3x^{2}+24x-51[/tex]
I hope this is useful for you
regards
