EXAMPLE 1 Graph an equation of a parabola

SOLUTION

STEP 1

Rewrite the equation in standard form.18

x = – Write original equation.

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Graph x = – y2. Identify the focus, directrix, and axis

of symmetry.

–8x = y2 Multiply each side by –8.

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.

EXAMPLE 1 Graph an equation of a parabola

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.

3 2

–

x2 = 4py Standard form, vertical axis of symmetry

x2 = 4( )y3 2

Substitute for p3 2

x2 = 6y Simplify.

Write an equation of the parabola shown.

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 32

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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. x2 = 2y

SOLUTION

(0, ), x = 0 , y = –12

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GUIDED PRACTICE for Examples 1 and 2

SOLUTION

Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

3. y = – x214

(0, –1 ), x = 0 , y = 1

GUIDED PRACTICE for Examples 1 and 2

SOLUTION

Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

4. x = – y213

( , 0), x = – , y = 033

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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

x2 = – 8ySOLUTION

6. Directrix: x = 4

y2 = – 16xSOLUTION

7. Focus: (–2, 0)

y2 = – 8xSOLUTION

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.

x2 = 12y

8. Focus: (0, 3)

SOLUTION