Download presentation

1
**Graph an equation of a parabola**

EXAMPLE 1 Graph an equation of a parabola 18 Graph x = – y2. Identify the focus, directrix, and axis of symmetry. SOLUTION STEP 1 Rewrite the equation in standard form. 18 x = – Write original equation. –8x = y2 Multiply each side by –8.

2
EXAMPLE 1 Graph an equation of a parabola STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y2 = 4px where p = –2. The focus is (p, 0), or (–2, 0). The directrix is x = –p, or x = 2. Because y is squared, the axis of symmetry is the x - axis. STEP 3 Draw the parabola by making a table of values and plotting points. Because p < 0, the parabola opens to the left. So, use only negative x - values.

3
EXAMPLE 1 Graph an equation of a parabola

4
**( )y EXAMPLE 2 Write an equation of a parabola**

Write an equation of the parabola shown. SOLUTION The graph shows that the vertex is (0, 0) and the directrix is y = –p = for p in the standard form of the equation of a parabola. 3 2 – x2 = 4py Standard form, vertical axis of symmetry x2 = 4 ( )y 3 2 Substitute for p 3 2 x2 = 6y Simplify.

5
GUIDED PRACTICE for Examples 1, and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 1. y2 = –6x SOLUTION (– , 0), x = , y = 0 3 2

6
GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 2. x2 = 2y SOLUTION (0, ), x = 0 , y = – 1 2

7
GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 14 3. y = – x2 SOLUTION (0, –1 ), x = 0 , y = 1

8
GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 4. x = – y2 13 SOLUTION ( , 0), x = – , y = 0 3 3 4

9
GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 5. Directrix: y = 2 SOLUTION x2 = – 8y 6. Directrix: x = 4 SOLUTION y2 = – 16x 7. Focus: (–2, 0) SOLUTION y2 = – 8x

10
GUIDED PRACTICE for Examples 1 and 2 Write the standard form of the equation of the parabola with vertex at (0, 0) and the given directrix or focus. 8. Focus: (0, 3) SOLUTION x2 = 12y

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google