Find the Properties y=1/2x^2

Problem

y=1/2*x2

Solution

1. Identify the function type, which is a quadratic function in the form y=a*x2+b*x+c Here, a=1/2 b=0 and c=0

2. Determine the vertex by using the formula x=−b/(2*a) Since b=0 the xcoordinate is 0 Substituting x=0 into the equation gives y=0 The vertex is (0,0)

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

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

5. Find the intercepts by setting x=0 for the yintercept and y=0 for the xintercept. Both result in the origin (0,0)

6. Determine the domain and range. The domain of any quadratic is all real numbers. Since the vertex is at (0,0) and it opens upward, the range is y≥0

Final Answer

Vertex: *(0,0), Axis of Symmetry: *x=0, Direction: Upward, Domain: *(−∞,∞), Range: *[0,∞)

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