Florida B.E.S.T. MA.912.AR.3
B.E.S.T. Standard (Benchmark Cluster)
Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
Florida B.E.S.T. Standards for Mathematics
Cluster contents
Benchmarks in This Standard
MA.912.AR.3 is a B.E.S.T. standard. These are the benchmarks under it.
- MA.912.AR.3.1
Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.
- MA.912.AR.3.10
Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.
- MA.912.AR.3.2
Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
- MA.912.AR.3.3
Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically o...
- MA.912.AR.3.4
Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical o...
- MA.912.AR.3.5
Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function.
- MA.912.AR.3.6
Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.
- MA.912.AR.3.7
Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.
- MA.912.AR.3.8
Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the...
- MA.912.AR.3.9
Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written de...
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students build quadratic equations or functions from contexts, tables, graphs, roots, and key features. They solve for unknown values, graph parabolas, and represent inequality solutions on number lines or in the coordinate plane.
What Mastery Looks Like
- A student can write a quadratic from a graph, table, roots, or context and move among standard, factored, and vertex forms. They choose an efficient solving method and check their roots. They graph key features and show inequality solutions with correct endpoints, intervals, or shaded regions.
Common Misconceptions
- Students may confuse zeros with the y-intercept, lose signs when factoring, or forget both square roots. They may shade the wrong side of a parabola or mishandle endpoints in inequality solutions.
How to Assess It
- Exit ticket: Given f(x) = x² − 4x − 5, rewrite it in factored form, find its zeros and vertex, sketch it, and solve f(x) ≤ 0.
Lesson moves
Ways to Teach It
Use algebra tiles to build x² + 5x + 6, arrange a rectangle, then connect its side lengths to factors and zeros.
Ask students to choose standard, factored, or vertex form for finding zeros, vertex, and y-intercept, then justify each choice.
Run a card sort matching each quadratic equation to its graph, vertex, zeros, and the solution set of a related inequality.
Model a thrown ball with h(t) = −16t² + 48t + 5, then find its maximum height and when it hits the ground.
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Printable MA.912.AR.3 Worksheet
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Related Standards
- MA.912.AR.5
Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
- MA.7.AR.2
Write and solve equations and inequalities in one variable.
- MA.912.AR.4
Write, solve and graph absolute value equations, functions and inequalities in one and two variables.
- MA.912.AR.2
Write, solve and graph linear equations, functions and inequalities in one and two variables.
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