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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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Parabola graphing

Vertical Axis of Symmetry

Horizontal Axis of Symmetry

Parabola - Graphing

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


Parabola graphing

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


Parabola graphing

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


Parabola graphing

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

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 graphing

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


Parabola graphing

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


Parabola graphing

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


Parabola graphing

Parabola - Graphing

END OF PRESENTATION

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