Chapter Test
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Which variable is raised to the second power? Does it mean that the axis of symmetry of the parabola is a horizontal or a vertical line?
Focus: ( 1/8, 0 )
Directrix: x=- 1/8
Axis of Symmetry: y=0
Before we begin, note that in the given equation the variable that is raised to the second power is y. x=2y^2 Therefore, the axis of symmetry of the parabola is a horizontal line.
Let's recall the general form of the equation for this type of parabola.
Knowing that p= 18, we can rewrite the equation. x=2y^2 ⇕ x=1/4( 18 ) (y- 0)^2+ 0 Now we have that p= 18, k= 0, and h= 0. By recalling the corresponding formulas, we can find the focus, directrix, and axis of symmetry of the parabola.
| Focus | Directrix | Axis of Symmetry | |
|---|---|---|---|
| Formula | ( h+ p, k) | x= h- p | y= k |
| Value | ( 0+ 1/8, 0) ⇒ ( 1/8,0 ) | x= 0- 1/8 ⇒ x=- 1/8 | y= 0 |
Now, let's draw the parabola using the obtained information.
