The value of k in the given function is k =3
From the question, the given function is F(x)= kx2
This can be properly written as
[tex]f(x) =kx^{2}[/tex]
Also, from the question, we have that f(2) = 12
Since [tex]f(x) =kx^{2}[/tex]
∴ [tex]f(2) =k(2)^{2}[/tex]
This becomes
[tex]f(2) = k \times 4[/tex]
[tex]f(2) = 4k[/tex]
Now, to determine the value of k, we will input the value of f(2), that is f(2)=12 in the above equation, that is
[tex]f(2) = 4k[/tex] becomes
[tex]12= 4k[/tex]
Now, divide both sides by 4
[tex]\frac{12}{4} = \frac{4k}{4}[/tex]
[tex]3 = k[/tex]
∴ [tex]k = 3[/tex]
Hence, the value of k in the given function is k =3
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