NY Next Generation Math AI-A.REI.7.a
The Standard
Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve a system containing one line and one parabola in Algebra I, with rational intersection coordinates. They use algebra and graphs to locate every common solution.
What Mastery Looks Like
- The student substitutes a linear expression into the quadratic equation, solves accurately, and finds each matching coordinate. A graph confirms the number and approximate location of intersections.
Common Misconceptions
- Students may solve for x but omit corresponding y-values or assume every line and parabola meet twice. They may use conics beyond the Algebra I parabola scope.
How to Assess It
- Ask students to solve y equals x plus 1 and y equals x squared minus 2x plus 1 algebraically, then confirm both rational intersections on a graph.
Lesson moves
Ways to Teach It
Overlay line and parabola graphs, mark intersections, and substitute those coordinates into both equations.
Ask students what zero, one, or two intersections mean for a linear-quadratic system.
Play intersection forecast by predicting solution counts before graphing line-parabola system cards.
Model when a linear boundary and parabolic path have the same height or position.
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Related Standards
- AII-A.REI.7.b
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- NY-8.EE.8.c
Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.
- AI-A.REI.6.a
Solve systems of linear equations in two variables both algebraically and graphically.
- NY-8.EE.8.b
Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases ...
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