Rewrite the expression $6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$?
+118608
Rewrite the expression \( 6j^2 - 4j + 12\) in the form \( c(j + p)^2 + q\), where c, p, and q are constants. What is \(\frac{q}{p}\)
\(6j^2-4j+12\\ =6(j^2-\frac{2}{3}j)+12\\ =6(j^2-\frac{2}{3}j+\frac{1}{9})+12-\frac{6}{9}\\ =6(j-\frac{1}{3})^2+11\frac{1}{3}\\ =6(j-\frac{1}{3})^2+11\frac{1}{3}\\ =6(j-\frac{1}{3})^2+\frac{34}{3}\\~\\ p=\frac{-1}{3}\qquad q=\frac{34}{3}\\ \frac{q}{p}=\frac{34}{3}\div\frac{-1}{3}\\ \frac{q}{p}=\frac{34}{3}\times\frac{3}{-1}=-34\\ \)
+118608
Rewrite the expression \( 6j^2 - 4j + 12\) in the form \( c(j + p)^2 + q\), where c, p, and q are constants. What is \(\frac{q}{p}\)
\(6j^2-4j+12\\ =6(j^2-\frac{2}{3}j)+12\\ =6(j^2-\frac{2}{3}j+\frac{1}{9})+12-\frac{6}{9}\\ =6(j-\frac{1}{3})^2+11\frac{1}{3}\\ =6(j-\frac{1}{3})^2+11\frac{1}{3}\\ =6(j-\frac{1}{3})^2+\frac{34}{3}\\~\\ p=\frac{-1}{3}\qquad q=\frac{34}{3}\\ \frac{q}{p}=\frac{34}{3}\div\frac{-1}{3}\\ \frac{q}{p}=\frac{34}{3}\times\frac{3}{-1}=-34\\ \)
