Graph y=x^2

Problem

y=x2

Solution

1. Identify the type of function. The equation y=x2 represents a basic quadratic function, which forms a curve known as a parabola.

2. Determine the vertex. Since the equation is in the form y=a*x2 the vertex is located at the origin (0,0)

3. Calculate several points to determine the shape. Choose x values on both sides of the vertex:

• If x=1 y=(1)2=1 Point: (1,1)

• If x=−1 y=(−1)2=1 Point: (−1,1)

• If x=2 y=(2)2=4 Point: (2,4)

• If x=−2 y=(−2)2=4 Point: (−2,4)

4. Plot the points (0,0) (1,1) (−1,1) (2,4) and (−2,4) on a coordinate plane.

5. Sketch a smooth, U-shaped curve passing through these points. The parabola opens upward because the coefficient of x2 is positive.

Final Answer

y=x2

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