Directions: Create a quadratic equation with the greatest possible maximum value using the digits 1 through 9, no more than one time each.

### Hint

### Hint

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

### Answer

### Answer

There are many solutions but a 9 must go into the last term as the k-value. That affects its y-axis position while the the a and h terms affect its width and x-axis position. Play with the sliders on this Desmos graph for a hands on way of understanding how the a, x, and k terms affect the quadratic: https://www.desmos.com/calculator/uffgbapfzf

Source: Robert Kaplinsky

What makes this problem a DOK 3? It seems too simple to be a DOK 3. Please help me understand. Thank you.

Hi Karen. I’m not going to win an award for a speedy response, but the reason it’s a DOK 3 is the optimization. It’s challenging enough to make a quadratic that (as an example) goes through a given point. However, to find the absolute maximum value requires much deeper understanding.