1 / 9

Parabola - Graphing

Vertical Axis of Symmetry. Horizontal Axis of Symmetry. Parabola - Graphing. Recall that the equations for a parabola are given by . Parabola - Graphing. The vertex of the parabola is located at the point (h, k) . Example 1: Determine the vertex of

lorene
Télécharger la présentation

Parabola - Graphing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Vertical Axis of Symmetry Horizontal Axis of Symmetry Parabola - Graphing • Recall that the equations for a parabola are given by ...

  2. Parabola - Graphing • The vertex of the parabola is located at the point (h, k). • Example 1: • Determine the vertex of • the parabola given by ... The vertex is at V(2, -3). • Geometrically, the vertex is the midpoint of the line segment joining the focus and the directrix. Slide 2

  3. Vertical Axis of Symmetry Horizontal Axis of Symmetry Parabola - Graphing • Note that when the squared term is in x, the axis of symmetry is vertical, and the parabola is facing up or down. • When the squared term is in y, the axis of symmetryis horizontal, and the parabola is facing left or right. Slide 3

  4. Parabola - Graphing • The value of p is the directed distance from the vertex to the focus. • Example 2: • Consider the parabola at • the right. • Since the parabola is facing down, the axis of symmetry is vertical and the equation is of the form ... • The distance from the vertex to the focus moves in a negative direction, implying that p  0. Slide 4

  5. Parabola - Graphing • Since the vertex is equidistant from the focus and the directrix (as are all points on the parabola by the definition), the distance from the vertex to the directix is • | p | units. • To determine the basic shape of the parabola, it is a good idea to plot one or more points other than the vertex. Slide 5

  6. 4 4 V (1, - 2) axis of symmetry y = - 2 - 4 Parabola - Graphing • Example 3: • Sketch the graph of the • parabola whose equation • is given at the right. • The vertex is at V(1, -2). • Since the square is on the y, the axis of symmetry is horizontal, with the parabola facing left or right ... Slide 6

  7. Parabola - Graphing • Find the value of p ... 4 • Since p is negative, the parabola is facing left. 4 - 4 • Plot another point. Letting y = 4 yields x = -2, or the point (-2, 4) ... Slide 7

  8. F (- 2, - 2) directrix x = 4 Parabola - Graphing • Sketch the graph using the points and the axis of symmetry ... 4 • Using p = -3 the focus is three units to the left of the vertex ... 4 • The directrix is a vertical line 3 units on the other side of the vertex. - 4 Slide 8

  9. Parabola - Graphing END OF PRESENTATION Click to rerun the slideshow.

More Related