Mississippi Math FA.F.22
The Standard
Graph a system of two functions, f(x) and g(x), on the same Coordinate Plane by hand for simple cases, and with technology for complicated cases. Explain the relationship between the point(s) of intersection and the solution to the system. Determine the solution(s) using technology, a table of values, substitution, or successive approximations. (Limited to linear and quadratic functions only.) (8.EE.7b, A-REI.6, A-REI.11)
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph two linear or quadratic functions on the same axes. They find where the graphs meet and explain that each meeting point works in both functions. They use a table, substitution, or graphing technology to find solutions that are hard to read from a graph.
What Mastery Looks Like
- A student can graph simple pairs by hand and use technology for harder pairs. They give every solution as an ordered pair and check it in both functions. They can also tell when the graphs never meet.
Common Misconceptions
- Students may give only the x-value instead of the full point. Some look for where each graph crosses the x-axis, rather than where the graphs cross each other. A graph that just touches another still has one solution.
How to Assess It
- Have students graph f(x)=x+2 and g(x)=x² on the same grid. Ask them to label every intersection and check each point in both equations.
Lesson moves
Ways to Teach It
Draw y=x+2 and y=x² on separate clear grid sheets, stack them on matching axes, and mark both crossings.
Graph y=0 and y=x², then ask partners why the graphs touching gives one solution, not two.
Race to find where y=2x+1 and y=x²+1 match in a table, then check each point by substitution.
Plot revenue R(x)=10x and cost C(x)=x²+3x+10 for 0 to 6 sales, then mark the break-even points.
Free download
Printable FA.F.22 Worksheet
A ready-to-print activity worksheet aligned to FA.F.22, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- FA.F.23
With accuracy, graph the solutions to a linear inequality in two variables as a half-plane, and graph the solution set to a system of linear inequalities in two...
- A-REI.11
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); fin...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson