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Understanding Parabolas: Focus, Directrix, and Equation Graphing

Explore the properties of parabolas, such as focus, directrix, vertex, and direction of opening. Learn how to write equations for parabolas and graph them accurately. Practice finding intersection points algebraically. This worksheet guides you through the process step by step.

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Understanding Parabolas: Focus, Directrix, and Equation Graphing

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  1. Warm Up April 17th 1. What is the focus and directrix? 2. What is the vertex and which direction does the parabola open?

  2. Week 13 #4

  3. Find the point(s) of intersection algebraically.

  4. Parabolas Writing equations

  5. If p is POSITIVE the parabola opens UP • If p is NEGATIVE the parabola opens DOWN When xis squared

  6. If p is POSITIVE the parabola opens RIGHT • If p is NEGATIVE the parabola opens LEFT When yis squared

  7. Graph what you have been given. • Find the p-value. • Identify h and k. • Write the equation. Writing the equation of the parabola

  8. Focus (0, 1) • Directrix: y = 5 1. Graph what you have. Find the p-value. Find (h, k). Graph Opens DOWN p = -2 So multiply it by 4.  V (0, 3)  F

  9. Focus (2, 0) • Directrix: x = -1 2. Graph what you have. Find the p-value. Find (h, k). Graph Opens RIGHT p = 1.5 So multiply it by 4. V (.5, 0)   F

  10. Focus (0, -5) • Directrix: y = 0 3. Graph what you have. Find the p-value. Find (h, k). Graph Opens DOWN p = -2.5 So multiply it by 4.  V (0, -2.5)  F

  11. Focus (-4, 0) • Directrix: x = -2 4. Graph what you have. Find the p-value. Find (h, k). Graph Opens LEFT p = -1 So multiply it by 4.  F  V (-3, 0)

  12. Vertex (0, 0) • Focus (0, -2) 5. Graph what you have. Find the p-value. Find (h, k). Graph Opens DOWN p = -2 So multiply it by 4.  V  F

  13. Vertex (0, 0) • Focus (0, -3) 6. Graph what you have. Find the p-value. Find (h, k). Graph Opens DOWN p = -3 So multiply it by 4.  V  F

  14. Focus(0, 4) • Directrix: x = -4 7. Graph what you have. Find the p-value. Find (h, k).  F  V Graph Opens RIGHT p = 2 So multiply it by 4.

  15. CW/HW worksheet

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