Graph f(x)=x^2

Problem

ƒ(x)=x2

Solution

1. Identify the function type as a basic quadratic function, which represents a parabola opening upwards.

2. Determine the vertex by using the standard form ƒ(x)=a*(x−h)2+k where a=1 h=0 and k=0 resulting in the vertex at (0,0)

3. Calculate several points to define the shape of the curve by substituting x values into the function.

4. Evaluate ƒ(1)=1=1 giving the point (1,1)

5. Evaluate ƒ*(−1)=(−1)2=1 giving the point (−1,1)

6. Evaluate ƒ(2)=2=4 giving the point (2,4)

7. Evaluate ƒ*(−2)=(−2)2=4 giving the point (−2,4)

8. Plot these points on a coordinate plane and connect them with a smooth, U-shaped curve.

Final Answer

ƒ(x)=x2

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