Florida B.E.S.T. MA.912.GR.7.4

MathGrades 9–12Apply geometric and algebraic representations of conic sections.

The Standard

Given a mathematical or real-world context, derive and create the equation of a parabola using key features.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students identify the vertex, axis, orientation, focus, directrix, or another known point. They use those features to determine the equation and explain how each value appears in it.
What Mastery Looks Like: Students can write a correct equation from a vertex, focus, directrix, point, graph, or context. They can verify the equation by checking its vertex, orientation, and focus distance.
Common Misconceptions: Students often confuse p with 4p in conic form. They may reverse the signs of h and k, choose the wrong orientation, or misread the focus distance.
How to Assess It: Give this exit ticket: “A parabola has vertex (2, -1) and focus (2, 3). Write its equation and identify its directrix.”

Lesson moves

On graph paper, mark a focus and directrix, construct equidistant points with a ruler, then use the vertex and p to write the equation.
Compare (x-2)^2=12(y+1) and (y+1)^2=12(x-2); explain how their orientations and key features differ.
Run a card sort matching feature sets, graphs, and equations; require students to justify each match using orientation and p.
Model a 12-foot-wide, 2-foot-deep satellite dish, place its vertex at the origin, derive its equation, and locate the receiver.

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