Please help, thank you so much.

Question

Consider the function f(x)=x^2+3x-18. Let g be a translation of f so that g has zeros x= -3 and x= -17. Write a rule for g.

Answer 1

f(x) = (x+3/2)^2 + 63/4

g(x) = (x+10)^2 -49

the vertex of f(x) is (-3/2, 15 3/4)

the vertex of g(x) is (-10, -49)

g(x) is f(x) shifted to the left by 8.5 and shifted down by 64.75

take the original equation x^2 + 3x + 18 and complete the square to

get (x+ 3/2)^2 + 63/4 by adding and subtracting 9/4

get g(x) by changing the sign of each zero, adding them to x, then multiplying those two together

(x+3)(x+17) = x^2 + 20x +51. Now complete the square again to get

(x+10)^2 -49 = g(x) by adding and subtracting 100 (half of 20 squared)