Florida B.E.S.T. MA.912.GR.7.8
The Standard
Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students translate a center, vertices, foci, asymptotes, or contextual measurements into the parameters of a hyperbola. They select a horizontal or vertical form and calculate missing values before writing the equation.
What Mastery Looks Like
- A student identifies the center, opening direction, and values of a and b from vertices, foci, or asymptotes. They choose the correct form, use c² = a² + b² when needed, and check the result against the given features.
Common Misconceptions
- Students often read (x − h) and (y − k) with the wrong center signs. They may make the wrong squared term positive or use a/b for every asymptote slope. They also confuse c² = a² + b² with the ellipse relationship.
How to Assess It
- Give this exit ticket: A hyperbola has center (2, −1), vertices (5, −1) and (−1, −1), and asymptotes y + 1 = ±(2/3)(x − 2). Write its equation and label a and b.
Lesson moves
Ways to Teach It
Use graph paper, rulers, and two marked foci to plot points with a fixed distance difference, then infer the center and vertices.
Write how changing the center, axis direction, or asymptote slope changes the form and graph of a hyperbola.
Sort cards showing graphs, equations, centers, vertices, and asymptotes, then justify each matched set to a partner.
Model a cooling tower cross-section from its center, narrowest width, and side slope, then write and check the equation.
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Related Standards
- MA.912.GR.7.2
Given a mathematical or real-world context, derive and create the equation of a circle using key features.
- MA.912.GR.7.6
Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.
- MA.912.GR.7.4
Given a mathematical or real-world context, derive and create the equation of a parabola using key features.
- MA.912.GR.7.9
Graph and solve mathematical and real-world problems that are modeled with an equation of a hyperbola. Determine and interpret key features in terms of the cont...
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