Graph y=-1/2x^2

Problem

y=−1/2*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2 which represents a parabola with its vertex at the origin (0,0)

2. Determine the direction of the opening. Since the coefficient a=−1/2 is negative, the parabola opens downward.

3. Calculate the vertical stretch or compression. The absolute value |a|=1/2 is less than 1 so the parabola is wider (vertically compressed) compared to the parent function y=x2

4. Find several points to plot by substituting x values into the equation.

5. Substitute x=0 y=−1/2*(0)2=0 Point: (0,0)

6. Substitute x=2 y=−1/2*(2)2=−2 Point: (2,−2)

7. Substitute x=−2 y=−1/2*(−2)2=−2 Point: (−2,−2)

8. Substitute x=4 y=−1/2*(4)2=−8 Point: (4,−8)

9. Plot the points (0,0) (2,−2) (−2,−2) (4,−8) and (−4,−8) on a coordinate plane and connect them with a smooth, downward-opening curve.

Final Answer

y=−1/2*x2

Want more problems? Check here!