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

x^2+3x-18 = (x+6)(x-3) with zeroes 3 and -6

(x+3)(x+17) = x^2 + 20x + 51 has zeroes -3 and -17

x^2+3x-18 = x^2 +3x + (3/2)^2 = 18+(3/2)^2

x+ 3/2 = + or - sqr(81/4)

x = -3/2 + or - 9/2 = -12/2 or 6/2 = -6 or 3

x^2 + 20x + 100 = -51+100 = 49

x+10 = sqr49

x = -10 + or - 7 = -17 or -3

1st equation is an upward opening parabola with vertex with x coordinate half way between the zeroes -6 and 3 = -3/2

it's y coordinate is -9/2 (3/2,-7)

2nd equation is also an upward opening parabola also with vertex with x coordinate half way between -17 and -3 = -10. (-10,-9/2)

the 1st equation's graph is shifted left by 8 1/2 (difference in x coordinates of the vertex)

and shifted down by 2 1/2 (difference in x coordinates of the vertex

rule to translate f to g is find the vertices and compare them