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Maximum Value of a Quadratic in Standard Form

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

Hint

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

Answer

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

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