Before we begin, note that in the given equation the variable that is raised to the second power is x.
y=2x^2
Therefore, the axis of symmetry of the parabola is a vertical line.
Finding the Desired Information
In order to match this form perfectly, let's rewrite our equation so that the parenthetical factor has a coefficient.
y=2x^2 ⇔ y=2(x-0)^2+0
We need to identify the values of h, k, and p. Let's start with p. To do so, we will solve the equation 14 p=2. We set it equal to 2, because 2 is the coefficient of the parenthetical factor.
Knowing that p= 18, we can rewrite the equation.
y=2x^2
⇕
y=1/4( 18 ) (x- 0)^2+ 0
Now we have that h= 0, k= 0, and p= 18. By recalling the corresponding formulas we can find the vertex, focus, directrix, and axis of symmetry of the parabola.
Vertex
Focus
Directrix
Axis of Symmetry
Formula
( h, k)
( h, k+ p)
y= k- p
x= h
Value
( 0, 0)
( 0, 0+ 1/8) ⇓ ( 0, 1/8 )
y= 0- 1/8 ⇓ y=- 1/8
x= 0
Drawing the Parabola
Now, let's draw the parabola using the obtained information.
