Florida B.E.S.T. MA.912.DP.2.8
The Standard
Fit a quadratic function to bivariate numerical data that suggests a quadratic association and interpret any intercepts or the vertex of the model. Use the model to solve real-world problems in terms of the context of the data.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide when a curved scatterplot supports a quadratic model and use technology to find an equation. They explain intercepts and the vertex using the data’s units and context. They use the model to predict values or find a maximum or minimum.
What Mastery Looks Like
- Given a data table or scatterplot, students can find a reasonable quadratic regression equation and use it to answer a context question. Their interpretation includes units, identifies a maximum or minimum, rejects irrelevant roots, and stays within a reasonable input range.
Common Misconceptions
- Students may choose a quadratic model without checking whether the scatterplot has a curved pattern. They may treat every root as meaningful or use the y-intercept when an input of zero makes no sense. They may swap vertex coordinates, confuse a maximum with a minimum, or predict far beyond the data range.
How to Assess It
- Exit ticket: A ball has heights 2, 18, 24, 20, and 6 feet at times 0, 1, 2, 3, and 4 seconds. Use quadratic regression, interpret the vertex, and estimate when the ball reaches the ground.
Lesson moves
Ways to Teach It
Record a tossed foam ball beside a meter stick, sample heights from video, run quadratic regression, and label the vertex and intercepts.
Present a scatterplot and model, then ask, “What makes a quadratic reasonable, and what do the vertex and intercepts mean here?”
Use a card sort matching data tables, scatterplots, equations, vertices, intercepts, and context statements, requiring students to justify each set.
Model profit versus ticket price from a small data table, then use the vertex to recommend a price and explain domain limits.
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