+267 Rewrite the expression 6j^2 - 4j + 12 in the form c(j + p)^2 + q, where c, p, and q are constants. What is q/p?
Quick help would be really appreciated
+9481 6j2 - 4j + 12 Factor out a 6 .
= 6(j2 - 2/3j + 2) Add and subtract (2/6)2
= 6( j2 - 2/3j + (2/6)2 + 2 - (2/6)2 ) Factor j2 - 2/3j + (2/6)2 as a perfect square trinomial.
= 6( (j - 2/6)2 + 2 - 4/36 ) Combine 2 and -4/36 .
= 6( (j - 1/3)2 + 17/9 ) Distribute the 6 .
= 6(j - 1/3)2 + 34/3
Now it is in the form c(j + p)2 + q , and q = 34/3 and p = -1/3 → q/p = (34/3) / (-1/3) = -34
+9481 6j2 - 4j + 12 Factor out a 6 .
= 6(j2 - 2/3j + 2) Add and subtract (2/6)2
= 6( j2 - 2/3j + (2/6)2 + 2 - (2/6)2 ) Factor j2 - 2/3j + (2/6)2 as a perfect square trinomial.
= 6( (j - 2/6)2 + 2 - 4/36 ) Combine 2 and -4/36 .
= 6( (j - 1/3)2 + 17/9 ) Distribute the 6 .
= 6(j - 1/3)2 + 34/3
Now it is in the form c(j + p)2 + q , and q = 34/3 and p = -1/3 → q/p = (34/3) / (-1/3) = -34
