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EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form. 1818 x = – Write original equation. 1818 Graph x = – y 2. Identify the focus, directrix, and axis of symmetry. – 8x = y 2 Multiply each side by – 8.

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EXAMPLE 1 Graph an equation of a parabola STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y 2 = 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.

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EXAMPLE 1 Graph an equation of a parabola

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EXAMPLE 2 Write an equation of a parabola 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. 3232 – x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 ( ) y 3232 Substitute for p 3232 x 2 = 6y Simplify. Write an equation of the parabola shown.

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GUIDED PRACTICE for Examples 1, and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 1. y 2 = –6x SOLUTION STEP 1 Rewrite the equation in standard form. y 2 = 4 (– )x 3 2

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GUIDED PRACTICE for Examples 1, and 2 STEP 2 Identify the focus, directrix, and axis of symmetry. The equation has the form y 2 = 4px where p = –. The focus is (p, 0), or (–, 0). The directrix is x = – p, or x =. Because y is squared, the axis of symmetry is the x - axis. 3 2 3 2 3 2

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GUIDED PRACTICE for Examples 1, and 2 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. 2.45 4.244.905.48

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GUIDED PRACTICE for Examples 1 and 2 Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 2. x 2 = 2y SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 SOLUTION STEP 1 Rewrite the equation in standard form. Write original equation. – 4y = x 2 Multiply each side by – 4. Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 3. y = – x 2 1414 y = – x 2 1414

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GUIDED PRACTICE for Examples 1 and 2 focus directrixaxis of symmetry x 2 = – 4 0, –1y = 1 Vertical x = 0 equation STEP 2

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GUIDED PRACTICE for Examples 1 and 2 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 y - values. y x 24.472.833.46 4

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GUIDED PRACTICE for Examples 1 and 2 SOLUTION STEP 1 Rewrite the equation in standard form. Write original equation. 3x = y 2 Multiply each side by 3. Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola. 4. x = – y 2 1313 1313 x = – y2y2

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GUIDED PRACTICE for Examples 1 and 2 focus directrixaxis of symmetry Horizontal y = 0 equation STEP 2 y 2 = 4 x 3 4 0, 3 4 x = – 3 4

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GUIDED PRACTICE for Examples 1 and 2 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. y x 1.733.872.453 3.46

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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 x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 ( –2)y Substitute –2 for p x 2 = – 8y Simplify. SOLUTION

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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. 6. Directrix: x = 4 y 2 = 4px Standard form, vertical axis of symmetry y 2 = 4 ( –4)x Substitute –4 for p y 2 = – 16x Simplify. SOLUTION

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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. 7. Focus: (–2, 0) y 2 = 4px Standard form, vertical axis of symmetry y 2 = 4 ( –2)x Substitute –2 for p y 2 = – 8x Simplify. SOLUTION

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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. x 2 = 4py Standard form, vertical axis of symmetry x 2 = 4 (3)y Substitute 3 for p x 2 = 12y Simplify. 8. Focus: (0, 3) SOLUTION

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