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=- x ⇔ - 1y^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=- 1. We set it equal to - 1 because - 1 is the coefficient of y^2.
Knowing that p= - 14, we can rewrite the equation.
y^2=- x
⇕
1/4( - 14 ) (y - 0)^2 + 0= x
Now we have that h= 0, k= 0, and p= - 14. 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+( - 1/4), 0) ⇕ ( - 1/4,0 )
x= 0-( - 1/4) ⇕ x=1/4
y= 0
Drawing the Parabola
Now, let's draw the parabola using the obtained information.
