Find the Properties y^2=-4x

Problem

y2=−4*x

Solution

1. Identify the form of the parabola. The equation y2=−4*x matches the standard form y2=4*p*x which represents a parabola opening horizontally.

2. Determine the value of p by comparing the coefficients.

4*p=−4

p=−1

3. Locate the vertex. Since there are no h or k offsets in the equation, the vertex is at the origin.

Vertex=(0,0)

4. Find the focus. For a horizontal parabola, the focus is located at (p,0)

Focus=(−1,0)

5. Identify the directrix. The directrix is a vertical line given by the equation x=−p

x=−(−1)

x=1

6. Determine the axis of symmetry. Since the parabola opens horizontally and the vertex is at the origin, the axis of symmetry is the x-axis.

y=0

7. Find the direction of opening. Because p<0 and the equation is in terms of y2 the parabola opens to the left.

Final Answer

Vertex: *(0,0), Focus: *(−1,0), Directrix: *x=1, Axis of Symmetry: *y=0, Opens: Left

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