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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

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Parabola - Graphing

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  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.

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