Graph an equation of a parabola

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Presentation transcript:

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.

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

( )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.

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

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

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

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

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

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