MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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11.1 Parabolas

Focus on parabola focus and parabola orientation.

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Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Focus and directrix of a parabolaWorked steps · five questions02Equation of a parabola from its featuresWorked steps · five questions
Lesson brief and rules

11.1 Parabolas

For y2=4y^{2}=4 px, the focus is (p,0)(p,0) and directrix is x=−px=-p.

Worked example 11
01 / Find the focus of y2=16xy^{2}=16x.
02 / Compare y2=4y^{2}=4 px: p=4p=4, focus (p,0)(p,0).
03 / Answer: (4,0)(4, 0)
Worked example 2 · Parabola orientation

Which direction does y2=−16xy^{2}=-16x open?

The coefficient 4p4p is negative, so p<0p<0. Answer: Left

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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