Quadratic Linear Systems
Authored by Paul Lofaso
Mathematics
9th - 10th Grade
CCSS covered
Used 486+ times
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About
This quiz focuses on solving systems of linear-quadratic equations, a fundamental topic in Algebra II typically taught in grades 9-10. The content requires students to understand the intersection points between linear functions and quadratic functions, which can result in zero, one, or two solutions depending on whether the line intersects, is tangent to, or misses the parabola entirely. Students must demonstrate mastery of multiple solution methods including graphical interpretation, algebraic substitution, and visual analysis of coordinate pairs. The problems assess students' ability to set equations equal to each other, solve resulting quadratic equations, substitute back to find y-coordinates, and interpret graphs accurately. Core skills include factoring quadratic expressions, using the quadratic formula when necessary, understanding the geometric relationship between parabolas and lines, and recognizing that the number of solutions corresponds to the number of intersection points on a coordinate plane. Created by Paul Lofaso, a Mathematics teacher in the US who teaches grades 9-10. This quiz serves as an excellent tool for formative assessment, allowing teachers to gauge student understanding of linear-quadratic systems before moving to more complex topics. The variety of question formats makes it versatile for multiple instructional purposes: the graphical interpretation questions work well as warm-up activities to activate prior knowledge, while the algebraic solving problems provide robust practice for homework assignments or in-class work sessions. Teachers can use this quiz for review before unit tests or as a diagnostic tool to identify students who need additional support with substitution methods or graphical analysis. The content directly aligns with Common Core standards A-REI.C.7, which requires students to solve systems consisting of linear and quadratic equations, and A-REI.D.11, which focuses on explaining why the x-coordinates of intersection points are solutions to equations formed by setting functions equal to each other.
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13 questions
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1.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Determine the number of solutions to the given linear-quadratic system.
0 solutions
1 solution
2 solutions
3 solutions
Tags
CCSS.HSA.REI.C.7
2.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
What are the solutions to the graphed system?
(0,-2) and (3,1)
(-2,0) and (2,0)
(0,-2) and (3,1)
(2,2) and (1,0)
Tags
CCSS.HSA.REI.C.7
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A
B
C
D
Tags
CCSS.HSA.REI.C.7
4.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Solve the system of linear and quadratic equations:
y = 5
y = 2x2 - 16x + 29
(6, 5) and (2, 5)
(2, 6)
(6, 2)
(5, 6) and (5, 2)
Tags
CCSS.HSA.REI.C.7
5.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Determine the number of solutions to the given linear-quadratic system.
Tags
CCSS.HSA.REI.C.7
6.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
What is the solution to the linear-quadratic system graphed in the picture.
(0, 0)
(3, 0)
(2, -3)
(-3, 2)
Tags
CCSS.HSA.REI.C.7
7.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A system that contains one linear function and one quadratic function can have 0, 1, or 2 solutions.
True
False
Cannot be determined
Nobody cares
Tags
CCSS.HSA.REI.C.7
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