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# Parabola - Graphing - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Parabola - Graphing' - lorene

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Presentation Transcript

Horizontal Axis of Symmetry

Parabola - Graphing

• Recall that the equations for a parabola are given by ...

• 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

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

• 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

• 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

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

• 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

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

END OF PRESENTATION

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