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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
- 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

- 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.

Slide 3

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 - 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

- 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

- 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

END OF PRESENTATION

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