Graph F(x)=x^2

Problem

F(x)=x2

Solution

1. Identify the function type as a basic quadratic function, which represents a parabola opening upwards with its vertex at the origin (0,0)

2. Determine the vertex by using the standard form y=a*(x−h)2+k where a=1 h=0 and k=0

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

4. Evaluate for x=−2 F*(−2)=(−2)2=4 giving the point (−2,4)

5. Evaluate for x=−1 F*(−1)=(−1)2=1 giving the point (−1,1)

6. Evaluate for x=0 F(0)=(0)2=0 giving the point (0,0)

7. Evaluate for x=1 F(1)=(1)2=1 giving the point (1,1)

8. Evaluate for x=2 F(2)=(2)2=4 giving the point (2,4)

9. Plot these points on a Cartesian coordinate system and connect them with a smooth, U-shaped curve.

Final Answer

F(x)=x2

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