Answer:
C
Step-by-step explanation:
The general rule for the quadratic function is
[tex]y=ax^2+bx+c[/tex]
From the graph you can see that the curve passes through the points (2,4), (1,7) and (3,7), so
[tex]y(2)=4\Rightarrow 4=a\cdot 2^2+b\cdot 2+c\\ \\y(1)=7\Rightarrow 7=a\cdot 1^2+b\cdot 1+c\\ \\y(3)=7\Rightarrow 7=a\cdot 3^2+b\cdot 3+c[/tex]
We get the system of three equations:
[tex]\left\{\begin{array}{l}4a+2b+c=4\\ \\a+b+c=7\\ \\9a+3b+c=7\end{array}\right.[/tex]
Subtract these equations:
[tex]\left\{\begin{array}{l}4a+2b+c-a-b-c=4-7\\ \\9a+3b+c-a-b-c=7-7\end{array}\right.\Rightarrow \left\{\begin{array}{l}3a+b=-3\\ \\8a+2b=0\end{array}\right.[/tex]
From the second equation:
[tex]b=-4a[/tex]
Substitute it into the first equation:
[tex]3a-4a=-3\\ \\a=3[/tex]
So,
[tex]b=-4\cdot 3=-12[/tex]
and
[tex]3+(-12)+c=7\\ \\c=7+9=16[/tex]
The quadratic function is
[tex]y=3\cdot x^2-12x+16[/tex]
