Answer:
A
Step-by-step explanation:
The general rule for the quadratic function is
[tex]y=ax^2+bx+c[/tex]
Use the data from the table:
[tex]y(0)=6\Rightarrow 6=a\cdot 0^2+b\cdot 0+c\\ \\y(1)=4\Rightarrow 4=a\cdot 1^2+b\cdot 1+c\\ \\y(-1)=10\Rightarrow 10=a\cdot (-1)^2+b\cdot (-1)+c[/tex]
We get the system of three equations:
[tex]\left\{\begin{array}{l}c=6\\ \\a+b+c=4\\ \\a-b+c=10\end{array}\right.[/tex]
From the first equation
[tex]c=6,[/tex] then
[tex]\left\{\begin{array}{l}a+b=-2\\ \\a-b=4\end{array}\right.[/tex]
Add these two equations:
[tex]a+b+a-b=-2+4\\ \\2a=2\\ \\a=1[/tex]
So,
[tex]b=-2-a=-2-1=-3[/tex]
The quadratic function is
[tex]y=1\cdot x^2-3x+6\\ \\y=x^2-3x+6[/tex]
