Graph y=-2x^2

Problem

y=−2*x2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2+b*x+c where a=−2 b=0 and c=0

2. Determine the shape and orientation. Since a=−2 is negative, the parabola opens downward. The magnitude |a|=2 indicates the parabola is narrower than the parent function y=x2

3. Find the vertex. For a function in the form y=a*x2 the vertex is at the origin (0,0)

4. Calculate additional points to determine the curve. Choose x values on both sides of the vertex:
   If x=1 y=−2*(1)2=−2 Point: (1,−2)
   If x=−1 y=−2*(−1)2=−2 Point: (−1,−2)
   If x=2 y=−2*(2)2=−8 Point: (2,−8)
   If x=−2 y=−2*(−2)2=−8 Point: (−2,−8)

5. Plot the points (0,0) (1,−2) (−1,−2) (2,−8) and (−2,−8) on a coordinate plane and connect them with a smooth, downward-opening curve.

Final Answer

y=−2*x2

Want more problems? Check here!