Problem of the Week - Algebra and Up - Dec. 20, 2020 to Dec. 26, 2020

Algebra and Up: 

Question: When a lemur leaps across the ground, it travels forward 30 feet and reaches a height of 10 feet in the air. Each leap takes 2 seconds from take-off to landing. Model the lemur's leap with the equation of a parabola in which x = the elapsed time in seconds and y = the height off the ground in feet. 

[Hint: A parabola in vertex form is written y = a(x – h)² + k when (h, k) is the vertex.]

Answer:   y = –10(x – 1)² + 10

Solution:  The vertex of a parabola that opens down, like the model of the leap, is the highest point. So, the vertex of our model will be (1, 10). To write our equation, we first plug h and k into our general form: y = a(x – 1)² + 10. Next, we use a known point on the parabola and plug those values in for x and y. Let’s use the origin: 0 = a(0 – 1)² + 10. If we solve for a, we get a = –10. So, our equation that models the leap is y = –10(x – 1)² + 10.

Note: Answers may vary with different domains and forms of the equation.