As posted on twitter.com/dmarain...
SHOW: The line with slope 1 intersecting y=-(x-h)²+k at its vertex also intersects at (h-1,k-1).
COREFLECTIONS
How would you modify this to make a grid-in or multiple choice question? A question similar to this appears on the published practice NEW PSAT. It is one of the last 3-4 questions on the grid-in with calculator section and was rated "medium" difficulty. I would rate it as more difficult! I recently tweeted the link for this practice test but easy to find on the College Board website.
Do the parameters h,k discourage use of graphing software?
Does the student need the equation of the line to solve the linear-quadratic system? Why does (h-1,k-1) have to be on the line? Then what?
What will be your source of questions like this for your students?
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2 comments:
One of the things with dynamic math software is what does show mean and will students see a need. Does this Desmos sketch show the result? https://www.desmos.com/calculator/0krudh5tl7
Outstanding DEMONSTRATION, John! Desmos beautifully uses sliders to allow investigations with parameters. Ideally we want our students to be able to show this algebraically and to use technology to verify and explore further. I'm a huge proponent of a balanced approach. Am I alone?
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