Let's recall the general form of a parabola whose axis of symmetry is a horizontal line.
1/4 p(y- h)^2+ k=x
In order to match this form perfectly, let's rewrite our equation a bit.
y^2=4x ⇔ 1/4y^2=x
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= 14. We set it equal to 14 because 14 is the coefficient of y^2.
Knowing that p= 1, we can rewrite the equation.
y^2=4x
⇕
1/4( 1 ) (y - 0)^2 + 0= x
Now we have that h= 0, k= 0, and p= 1. 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+ p, k)
x= h- p
y= k
Value
( 0, 0)
( 0+ 1, 0) ⇕ (1,0 )
x= 0- 1 ⇕ x=- 1
y= 0
Drawing the Parabola
Now, let's draw the parabola using the obtained information.
