Respuesta :
Answer:
[tex]100a+10b+c=-55[/tex]
Step-by-step explanation:
Solve for c for each coordinate point:
[tex]f(x)=ax^2+bx+c[/tex]
[tex]0=ax^2+bx+c[/tex]
[tex]0=a(-1)^2+b(-1)+c[/tex]
[tex]0=a-b+c[/tex]
[tex]-c=a-b[/tex]
[tex]c=b-a[/tex]
[tex]f(x)=ax^2+bx+c[/tex]
[tex]5=a(0)^2+b(0)+c[/tex]
[tex]5=c[/tex]
[tex]f(x)=ax^2+bx+c[/tex]
[tex]0=a(5)^2+b(5)+c[/tex]
[tex]0=25a+5b+c[/tex]
[tex]-c=25a+5b[/tex]
[tex]c=-25a-5b[/tex]
Combine first and third equations to solve for b:
[tex]b-a=-25a-5b[/tex]
[tex]6b-a=-25a[/tex]
[tex]6b=-24a[/tex]
[tex]b=-4a[/tex]
Substitute values of b=-4a and c=5 to solve for a:
[tex]c=b-a[/tex]
[tex]5=-4a-a[/tex]
[tex]5=-5a[/tex]
[tex]-1=a[/tex]
Find b:
[tex]c=b-a[/tex]
[tex]5=b-(-1)[/tex]
[tex]5=b+1[/tex]
[tex]4=b[/tex]
Evaluate required expression:
[tex]100a+10b+c[/tex]
[tex]100(-1)+10(4)+5[/tex]
[tex]-100+40+5[/tex]
[tex]-60+5[/tex]
[tex]-55[/tex]
Therefore, [tex]100a+10b+c=-55[/tex]
