9.2 - Parabolas

1. 9.2 - Parabolas Objectives: Write and graph the standard equation of a parabola given sufficient information. Given an equation of a parabola, graph it and label the vertex, focus, and directrix. Standard: 2.8.11.E. Use equations to represent curves.

2. Parabolas A parabola is defined in terms of a fixed point, called the focus, and a fixed line, called the directrix. A parabola is the set of all points P(x, y) in the plane whose distance to a fixed point, called the focus, equals its distance to the fixed line, called the directrix. Recall from lesson 5.1, that the axis of symmetry of a parabola goes through the vertex and divides the parabola into two equal parts. The axis of symmetry also contains the focus and is perpendicular to the directrix. The vertex of a parabola is the midpoint between the focus and the directrix.

3. Parabola

4. Standard Equation for a Parabola The standard equation for a parabola with its vertex at the origin is: Horizontal Directrix Vertical Directrix p > 0: opens upward p < 0: opens downward focus: (0, p) directrix: y = -p Axis of symmetry: y-axis p > 0: opens right p < 0: opens left focus: (p, 0) directrix: x = -p Axis of symmetry: x-axis

6. Example 1b ** Graph . Label the vertex, focus, and directrix.

7. When you know the locations of any two of the three main characteristics of a parabola (focus, vertex, and directrix), you can write an equation for the parabola.

9. Example 2b Write the standard equation of the parabola with its vertex at the origin and with the directrixx=6.

11. Example 3a** Write the standard equation of the parabola graphed below.

12. Example 3b** Write the standard equation of the parabola with its focus at (-6, 4) and with the directrix x = 2.

13. Example 4a

14. Example 4b Graph the parabola . Label the vertex, focus, and directrix.

17. Homework Pg. 576-577 #10-46 even