Graph y^2=-1/4x

Problem

y^2=−1/4*x

Solution

1. Identify the type of conic section. Since the equation is in the form y^2=4*p*x it represents a parabola that opens horizontally.

2. Determine the direction of the opening. Because the coefficient of x is negative, the parabola opens to the left.

3. Find the value of p by setting the coefficient equal to 4*p

4*p=−1/4

p=−1/16

4. Locate the vertex. Since there are no h or k shifts, the vertex is at the origin.

Vertex=(0,0)

5. Identify the focus and directrix using p The focus is at (p,0) and the directrix is x=−p

Focus=(−1/16,0)

Directrix:x=1/16

6. Calculate additional points to define the width. If x=−4

y^2=−1/4*(−4)

y^2=1

y=±1

The points (−4,1) and (−4,−1) are on the graph.

Final Answer

y^2=−1/4*x

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