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Presentation transcript:

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

The vertex of the parabola is located at the point (h, k). 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

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 symmetry is horizontal, and the parabola is facing left or right. Vertical Axis of Symmetry Horizontal Axis of Symmetry Slide 3

The value of p is the directed distance from the vertex to the focus. 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

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

parabola whose equation is given at the right. Parabola - Graphing Example 3: Sketch the graph of the parabola whose equation is given at the right. 4 - 4 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 ... V (1, - 2) axis of symmetry y = - 2 Slide 6

Since p is negative, the parabola is facing left. 4 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

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

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