Find the Properties y=1/8x^2

Problem

y=1/8*x2

Solution

1. Identify the type of function. This is a quadratic function in the standard form y=a*x2+b*x+c where a=1/8 b=0 and c=0

2. Determine the direction of opening. Since the leading coefficient a=1/8 is positive, the parabola opens upward.

3. Find the vertex. For a parabola in the form y=a*x2 the vertex is located at the origin (0,0)

4. Identify the axis of symmetry. The axis of symmetry is the vertical line passing through the vertex, which is x=0

5. Calculate the focus. The distance from the vertex to the focus is p=1/(4*a)

p=1/(4*(1/8))

p=2

Since it opens upward, the focus is at (0,p) which is (0,2)

6. Determine the directrix. The directrix is a horizontal line p units below the vertex, given by y=−p

y=−2

7. Find the focal diameter (latus rectum length). The length is given by |4*p|

|4*(2)|=8

Final Answer

y=1/8*x2⇒Vertex: *(0,0), Focus: *(0,2), Directrix: *y=−2, Axis of Symmetry: *x=0

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