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