What is this equation, equivalent to c(x)=(x+6)^2+14

Work Shown:

c(x) = (x+6)^2+14

c(x) = (x+6)(x+6)+14

c(x) = x(x+6)+6(x+6)+14

c(x) = x^2+6x+6x+36+14

c(x) = x^2+12x+50

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: