Consider the function f(x) = x^2 + 3x − 18. Let g be a translation of f so that g has zeros x = −10 and x = −1. 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 = −10 and x = −1. Write a rule for g.

Answer 1

f(x) = x^2 + 3x - 18 = (x+6)(x-3) has 0s at -6 and 3. g has zeroes at -10 and -1. The zeroes have moved 4 to the left. Thus, let g(x) = f(x+4)

To show that this works, g(-10) = f(-10 + 4) = f(-6) = 0; g(-1) = f(-1+4) = f(3) = 0