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EXAMPLE 1

18. 18. STEP 1. Rewrite the equation in standard form. x = –. EXAMPLE 1. Graph an equation of a parabola. Graph x = – y 2 . Identify the focus, directrix, and axis of symmetry. SOLUTION. Write original equation. Multiply each side by – 8 . –8 x = y 2. STEP 2. STEP 3.

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EXAMPLE 1

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

  2. STEP 2 STEP 3 Identify the focus, directrix, and axis of symmetry. The equation has the form y2 = 4pxwhere p = –2. The focus is (p, 0), or (–2, 0). The directrix is x = –p, or x = 2. Because yis squared, the axis of symmetry is the x - axis. 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. EXAMPLE 1 Graph an equation of a parabola

  3. EXAMPLE 1 Graph an equation of a parabola

  4. Write an equation of the parabola shown. 3 2 3 2 The graph shows that the vertex is (0, 0) and the directrix is y = –p = for pin the standard form of the equation of a parabola. – ( )y 32 x2 = 4 Substitute for p EXAMPLE 2 Write an equation of a parabola SOLUTION x2 = 4py Standard form, vertical axis of symmetry x2 = 6y Simplify.

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

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

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

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

  9. for Examples 1 and 2 GUIDED PRACTICE 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 x2 = – 8y SOLUTION 6. Directrix: x = 4 y2 = – 16x SOLUTION 7. Focus: (–2, 0) y2 = – 8x SOLUTION

  10. for Examples 1 and 2 GUIDED PRACTICE 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) x2 = 12y SOLUTION

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