In planning her retirement, liza deposits some money at 4.5% interest, with twice as much deposited at 5%. find the amount deposited at each rate if the total annual interest income is $2755. she deposited $ at 4.5% and $ at 5%.

For this problem, we can assume that we deposits X money at 4.5% interest, than we can know that 2X were deposited at 5% interest, therefore we can get the equation of:  4.5%*X+5%*2X=2755, than we can get X=19000, so the 2X=38000, than we can concluded that: she deposited $19000 at 4.5% and $38000 at 5%.

The vertex of the quadratic function is (1.5, -.75)