Home > High School: Functions > Maximum Value of a Quadratic in Vertex Form

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.

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

Print Friendly, PDF & Email

Check Also

Creating Sequences

Directions: Using the digits 0-9, at most one time each, complete the first three terms …

3 comments

  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.

Leave a Reply

Your email address will not be published. Required fields are marked *