Precalculus (Parabola) Second quarter for senior high school stem strand.pptx

This is a topic in precalculus 1st quarter.

1. Parabola Prepared by: Josephine e. patac

2. PRELIMINARY ACTIVITY

3. Equation of a vertical or Horizontal Parabola with Vertex at the Origin Parabola opens Upward Focus (0,a) Directrix y = -a Equation   Parabola opens Downward Focus ( 0, -a) Directrix y = a Equation  

4. Parabola opens to the right Focus (a, ) Directrix x = -a Equation   Parabola opens to the left Focus (-a, ) Directrix x = a Equation  

5. Standard form of the equation of a parabola with vertex at the origin

6. ACTIVITY Direction: Sketch the Graph of the parabola given the equations with vertex at the origin. Label all the features. 1. 2.  

7. Standard of the equation of a parabola with vertex at (h, K)

8. ACTIVITY: Direction: Sketch the graph of the following functions.Label and identify the parts. 1. 2. 3. 4.  

9. I. TRUE or FALSE. Write “ T ” if the statement is true, and “ F ” if the statement is false. 1. A latus rectum is a segment on the parabola passing through the focus (F) and perpendicular to the directrix. 2. The focus and directrix are units above and below the vertex. 3. The distances of the point P from the focus and from the directrix are equal. 4. The vertex is the point midway between the focus and the directrix. 5. If the parabola opens downward, the vertex is the lowest point. If the parabola opens upward, the vertex is the highest point.

10. 6. The directrix is c units below or above the vertex. 7. The focus is c units above or below the vertex. 8. Any point on the parabola has the same distance from the focus as it has from the directrix. 9. The latus rectum is a line that divides the parabola into two parts that passes through the focus which results to mirror images of each other. 10.A latus rectum is a line on the parabola passing through the focus (F) and parallel to the directrix.

11. II. Below is a table representation of the equations, graphs, and other properties of a parabola. Complete the table by filling in the numbered cells what is missing.

12. III.

13. II V . Besides satellite dishes, and searchlights, where else do you see the concept of parabolas are being used? Briefly state your answer.

14. ANSWER KEY: I.true or false 1. T 2. T 3. T 4. T 5. F 6. T 7. F 8. T 9. F 10. T

15. II. 1. Opening Downward 2. y = a 3. x = 0 4. Opening Upward 5. (, a) 6. Opening to the Left 7. x = a 8. y = 9. (a, 0) 10. x = a

16. III.