Directions: Create three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.

### Hint

How does changing the values of a, b, and c affect the graph? How can we ensure that the graph is symmetrical across x=4?

### Answer

Originally the problem was going to call for two equations but then I realized that it could be as simply as multiplying the a and c values by -1. There are infinite answers, and here are three of them: y = (x-4)^2 – 1, y = -(x-4)^2 + 1, y = -3(x-4)^2 + 3.

Source: Robert Kaplinsky

The answers given appear to be incorrect – the min/max values appear to be switched on the equations. I think the correct answers should be (x-4)^2 – 1, -(x-4)^2 + 1, -3(x-4)^2 + 3.

Thanks for the correction. The problem has been updated.