Answer:
Correct choice is B
Step-by-step explanation:
All given options represent quadratic function. Let the equation of this quadratic function be
[tex]f(x)=ax^2+bx+c.[/tex]
Then
1. [tex]f(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2;[/tex]
2. [tex]f(1)=7.5=a\cdot 1^2+b\cdot 1+c\Rightarrow 7.5=a+b+2;[/tex]
3. [tex]f(2)=12=a\cdot 2^2+b\cdot 2+c\Rightarrow 12=4a+2b+2.[/tex]
Solve the system of two equations:
[tex]\left\{\begin{array}{l}a+b+2=7.5\\4a+2b+2=12\end{array}\right.\Rightarrow\left\{\begin{array}{l}a=5.5-b\\4(5.5-b)+2b=10\end{array}\right.[/tex]
Then
[tex]22-4b+2b=10,\\ \\-2b=-12,\\ \\b=6,\\ \\a=5.5-6=-0.5.[/tex]
Thus, the equation of the function is
[tex]f(x)=-\dfrac{1}{2}x^2+6x+2.[/tex]
Note that
[tex]f(3)=-\dfrac{1}{2}\cdot 3^2+6\cdot 3+2=-4.5+20=15.5;[/tex]
[tex]f(4)=-\dfrac{1}{2}\cdot 4^2+6\cdot 4+2=18.[/tex]
