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Algebra II Items to Support Formative Assessment
Unit 3: Expanding Understanding of Quadratic Functions
Solve Systems of Equations
A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically. (Cross-cutting)
A.REI.C.7 Task
Farrell the frog spots a grasshopper 30 cm in front of him. He thought it would make a tasty
brunch. He jumps to catch the grasshopper and reaches a maximum height of 25 cm and travels a
horizontal distance of 35 cm. Gia the grasshopper, unaware of Farrell, was scavenging for her
own snack. She spots a zucchini flower on the plant 50 cm ahead and 10 cm above ground. She
jumps aiming for her snack.
a. Assume that Farrell’s starting position is at the origin of a coordinate grid. Use curve fitting to
write a quadratic equation that models Farrell’s jump path.
b. Determine the linear equation that models Gia’s jump path.
c. Will Gia become Farrell’s Sunday brunch or will she safely get to her tasty snack. Use
mathematics to support your answer.
Answer:
a. y = -
1 2 10
x + x
49
7
1
5
b. y = (x - 30)
c. Farrell will catch Gia. The zucchini flower is 80 cm away from Farrell. The system has a
solution at (64.741, 6.948), which means he will catch Gia when they are both 6.948 cm in the
air and have a horizontal distance of 64.741 cm.
A.REI.C.7 Item 1
Examine each of the following systems of equations:
1. y = 2x² - 8x + 6
2. y + 3x = 2
y + 2 = -½x
y = 3x² + x - 2
3. y = 3x + 3
y = 4x² + 2x + 3
Part A: Match each given system with the appropriate graphs.
a.
b.
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c.
Part B: Find the solution(s) for each given system.
Answers:
Part A
1.b 2.c 3. a
Part B
1. no solution 2. (-2, 8) and (2/3, 0) 3. (0, 3)
A.REI.C.7 Item 2
Solve the system of equations algebraically y= x2-x-6 and 2y=3x.
Answer: (4,0) and (−3/2,0)
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
A.REI.C.7 Item 3
a. The equation y = 6x 2 + 11x + 4 forms a system of equations with a solution at (−2, 6) with
which of the following linear equations?
y=-x+2
y = - 3x
y = 5x + 16
b. Find the other solution for the equation(s) you selected above.
Answers:
a. y = - 3x, y = 5x + 16
b. The system y = 6x 2 + 11x + 4 , y = - 3x has another solution at (−1/3, 1)
The system y = 6x 2 + 11x + 4 , y = 5x + 16 has another solution at (1, 21)
A.REI.C.7 Item 4
For the system of equations y = 3x2 + 6x - 13 and y = k, what are all the values of k so that the
system has:
a. one solution
b. two solutions
c. no solutions
Answers:
a. k = -16
b. k > -16
c. k < -16
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.