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Maximum Value of a Quadratic in Vertex Form

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



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



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

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

    • Robert Kaplinsky

      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.

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