Graph y=1/4x^2

Problem

y=1/4*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 which represents a parabola that opens upward because the coefficient a=1/4 is positive.

2. Determine the vertex. Since there are no horizontal or vertical shifts, the vertex is at the origin (0,0)

3. Calculate several points to determine the shape. Choose x values that are easy to calculate, such as multiples of 2.

4. Substitute x=2

y=1/4*(2)2

y=1/4*(4)

y=1

This gives the point (2,1)

5. Substitute x=4

y=1/4*(4)2

y=1/4*(16)

y=4

This gives the point (4,4)

6. Apply symmetry across the y-axis. Since the parabola is symmetric, the points (−2,1) and (−4,4) are also on the graph.

7. Plot the points (0,0) (2,1) (−2,1) (4,4) and (−4,4) and connect them with a smooth, wide curve.

Final Answer

y=1/4*x2

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