CCSS.Math.Content.HSG-GPE.A.2
The standard
Derive the equation of a parabola given a focus and directrix.
Common Core State Standards for Mathematics
What this standard means
Students need to build the equation of a parabola from its definition: points that are the same distance from a fixed point and a fixed line. They should set the distance to the focus equal to the distance to the directrix, then simplify into a standard equation.
Mastery looks like choosing the right distance expression, handling horizontal and vertical directrices, and explaining why the vertex sits halfway between the focus and directrix. Students often get stuck with signs, squaring both sides, and mixing up whether the parabola opens up, down, left, or right.
Ways to teach it
- Use graph paper, a ruler, and a given focus and directrix to plot several points equal distance from both, then sketch the parabola.
- Ask students to explain why the vertex must be halfway between the focus and directrix using a diagram and one sentence.
- Give one focus and one directrix, then have students write the first distance equation before doing any algebra.
- Connect to satellite dishes by showing how a cross section is a parabola with a focus that collects reflected signals.
Plan a lesson for CCSS.Math.Content.HSG-GPE.A.2
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