Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create a quadratic equation with the greatest possible maximum value.

### Hint

Where is the best place to put the 9? How does each box affect the graph’s behavior?

### Answer

The quadratic with the greatest possible maximum value is -x^2 + 9x + 8. Play with the sliders on this Desmos graph for a hands on way of understanding how the a, b, and c terms affect the quadratic: https://www.desmos.com/calculator/kdsj3ic0gn

Source: Robert Kaplinsky