Given:
Quadratic function is
[tex]f(x)=x^2-6x+c[/tex]
It passes through B(-2,4).
To find:
The value of c.
Solution:
The quadratic function passes through B(-2,4), it means the equation of quadratic equation must be true for the point B(-2,4).
We have,
[tex]f(x)=x^2-6x+c[/tex]
Putting x=-2 and f(x)=4, we get
[tex]4=(-2)^2-6(-2)+c[/tex]
[tex]4=4+12+c[/tex]
[tex]4=16+c[/tex]
Subtract both sides by -16.
[tex]4-16=c[/tex]
[tex]-12=c[/tex]
The value of c is -12.
Therefore, the correct option is A.
