CCSS.MATH.CONTENT.HSA.APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

CCSS.MATH.PRACTICE.MP4  Model with mathematics.

Task:

A ball is thrown up into the air at 6 feet per second from the ground.  At what point will the ball come back down and hit the ground?  (Hint: use 16 to represent gravity)  Write out all of your steps used in solving and graph the ball’s motion.

 

Commentary:

Learning how to use quadratics and how to find their roots can be very confusing to students at first.  When the vocabulary words roots and zeros of quadratic functions are first introduced students often do not create their own visualization of what these terms mean.  Students also do not realize that these words are interchangeable or what the purpose of finding them is.  This task gives them the opportunity to see one application of a quadratic function and also gives students the chance to visualize what the roots of a quadratic actually are.  Teachers may use this task while teaching students about the zeroes of polynomials and to show students how to model using mathematics.  This task should be given to students after they have been introduced to the methods used in finding the roots of a quadratic function.  This task is designed to give students a tangible scenario that will help them meet the common core standards.

 

Solution:

B (t) = -16t^2+6t

0 = t (-16t + 6)                 Factor out a t from both                                              terms and set equal to 0                                              to find the zeros of the                                                function.

0=t,  = t                             To find the t values, set                                               each factor equal to                                                     zero and solve for t

After (6/16) seconds the ball will fall back down and hit the ground.