Florida B.E.S.T. MA.912.AR.3.9
The Standard
Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a parabolic boundary and a shaded region into an inequality using x and y. They also translate phrases such as above, below, at most, and including the boundary into inequality symbols.
What Mastery Looks Like
- Given a graph, students identify the quadratic boundary and select <, ≤, >, or ≥ from the shading and boundary line. From a written context, they define variables, write the inequality, and check it with a reasonable point.
Common Misconceptions
- Students may shade the wrong side or choose a strict inequality when the boundary should be included. They may write only an equation, or misread the parabola's shift, reflection, or width. In context problems, they may ignore limits on possible values.
How to Assess It
- Exit ticket: A dashed parabola has equation y = (x - 2)² - 3, with the region below it shaded. Write the inequality and explain your symbol choice.
Lesson moves
Ways to Teach It
Give students transparent coordinate grids to trace a parabola, test three points, and shade all points that satisfy a given inequality.
Ask students to compare y < x² - 4 and y ≥ x² - 4, then explain how the boundary and shading change.
Use matching cards with quadratic inequalities, shaded graphs, and test points, and have pairs justify each completed set.
Model the space beneath a bridge arch from given measurements, then write an inequality showing where a vehicle could fit.
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