Step 1 :Since the points (-1,13), (0,6), and (1,2) are on the graph, we can form three equations:
Step 2 :\(-a+b+c=13\)
Step 3 :\(c=6\)
Step 4 :\(a+b+c=2\)
Step 5 :Substitute \(c=6\) into the first and third equations, we get:
Step 6 :\(-a+b+6=13\)
Step 7 :\(a+b+6=2\)
Step 8 :Solving these two equations, we get \(a=-3\) and \(b=-1\).
Step 9 :So the quadratic model for the function j is \(y=-3x^2-x+6\).
Step 10 :To predict the value of \(j(1.5)\), substitute \(x=1.5\) into the equation, we get \(j(1.5)=-3(1.5)^2-(1.5)+6\).
Step 11 :After calculation, we get \(j(1.5)=\boxed{-1.75}\).