[HELP] Consider the function f(x)=x^2+3x−18. Let g be a translation of f so that g has zeros x=−6 and x=−13. Write a rule for g.

Question

Consider the function f(x)=x^2+3x−18. Let (g) be a translation of f so that g has zeros x=-6 and x=-13. Write a rule for g.

Answer 1

g(x) = f(x - h) + k = (x - h)² + 3(x - h) - 18 + k.

Translation don't change type of function and coefficient of x² left the same 1.

So, g(x) = (x + 6)(x + 13) = x² + 19x + 78