Graph y^2=1/2x

Problem

y2=1/2*x

Solution

1. Identify the type of conic section. The equation is in the form y2=4*p*x which represents a parabola that opens to the right along the x-axis.

2. Determine the value of p to find the focus and directrix. Set 4*p=1/2

4*p=1/2

p=1/8

3. Locate the vertex. Since there are no h or k shifts, the vertex is at the origin (0,0)

4. Find the focus and directrix. The focus is at (p,0) which is (1/8,0) The directrix is the vertical line x=−p which is x=−1/8

5. Calculate additional points to define the width. If x=2 then y2=1/2*(2)=1 so y=±1 This gives the points (2,1) and (2,−1)

6. Sketch the curve. Draw a smooth curve starting at (0,0) passing through (2,1) and (2,−1) opening to the right.

Final Answer

y2=1/2*x⇒x=2*y2

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