IM Alg1.7.1 Lesson: Finding Unknown Inputs

A mechanical device is used to launch a potato vertically into the air. The potato is launched from a platform 20 feet above the ground, with an initial vertical velocity of 92 feet per second. The function models the height of the potato over the ground, in feet, seconds after launch. Here is the graph representing the function. For each question, be prepared to explain your reasoning. What is the height of the potato 1 second after launch?

8 seconds after launch, will the potato still be in the air?

Will the potato reach 120 feet? If so, when will it happen?

When will the potato hit the ground?

Your teacher will give you a picture that is 7 inches by 4 inches, a piece of framing material measuring 4 inches by 2.5 inches, and a pair of scissors. Cut the framing material to create a rectangular frame for the picture. The frame should have the same thickness all the way around and have no overlaps. All of the framing material should be used (with no leftover pieces). Framing material is very expensive! You get 3 copies of the framing material, in case you make mistakes and need to recut. Han says, “The perimeter of the picture is 22 inches. If I cut the framing material into 9 pieces, each one being 2.5 inches by inch, I’ll have more than enough material to surround the picture because those pieces would mean 22.5 inches for the frame.” Do you agree with Han? Explain your reasoning.

Write an equation to represent the relationship between the measurements of the picture and of the frame, and the area of the framed picture. Be prepared to explain what each part of your equation represents.

What would a solution to this equation mean in this situation?