Name_________________________________________________________
CCSS
A.REI.4
Date __________
Hitting a Baseball
You hit a baseball. The function h = −16t 2 + 75t + 3 gives the height h
(in feet) of the baseball after t seconds.
1. At what height is the baseball hit?
2. How long does it take for the baseball to reach a height of 25 feet? Find
your answer algebraically. Which method(s) did you use?
3. Does the baseball reach a height of 100 feet? Without using a graph, how
do you know?
4. How long does it take for the baseball to reach its maximum height?
5. How long does it take for the baseball to hit the ground? Find your answer
algebraically. Which method(s) did you use?
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Big Ideas Math
Performance Tasks
5
CCSS
A.REI.4
Common Core Georgia Performance Standard
A.REI.4 Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic
equation in x into an equation of the form ( x − p) 2 = q that has the
same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x 2 = 49 ), taking
square roots, completing the square, the quadratic formula and
factoring, as appropriate to the initial form of the equation. Recognize
when the quadratic formula gives complex solutions and write them as
a ± bi for real numbers a and b.
CCSS
A.REI.4
Grading Rubric
Answers
Score
1. 3 ft
1
2. after about 0.3 and 4.4 sec; Sample answer: quadratic formula
3
3. no; Sample answer: Write the equation −16t 2 + 75t + 3 = 100
and find the value of the discriminant, which is less than 0. So, the
equation has no real solutions.
2
4. about 2.3 sec
1
5. about 4.7 sec; Sample answer: quadratic formula
2
Precision
1
1. Student identifies the y-intercept of the function.
2. Student substitutes 25 for h, solves the resulting quadratic
2
equation, and identifies the method used. Student realizes that
there are two solutions.
3. Student understands how to determine if the baseball reaches a
2
certain height algebraically and recognizes when the quadratic
formula gives no real solutions.
1
4. Student identifies the x-coordinate of the vertex of the function.
5. Student substitutes 0 for h, solves the resulting quadratic equation,
and identifies the method used.
Total Points
6
Big Ideas Math
Performance Tasks
2
17
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