Respuesta :
Answer:
D. 12
Step-by-step explanation:
We have been given a function [tex]f(x)=cx^{2}+30[/tex], where c is a constant and f(3)= 12.
To find f(-3) we will find value of c by substituting value of f(3) in our given function.
[tex]12=c\times 3^{2}+30[/tex]
[tex]12=9c+30[/tex]
[tex]12-30=9c[/tex]
[tex]9c=-18[/tex]
[tex]c=\frac{-18}{9} =-2[/tex]
Upon substituting value of c in our given function we will get our function as [tex] f(x)=-2x^{2}+30[/tex]
Now let us find f(-3) by substituting x=-3 in our function.
[tex]f(-3)=-2(-3)^{2}+30[/tex]
[tex]f(-3)=-2(9)+30[/tex]
[tex]f(-3)=-18+30[/tex]
[tex]f(-3)=12[/tex]
Therefore, f(-3) is 12 and option D is the correct choice.
