Graph y=-x^2+2

Problem

y=−x2+2

Solution

1. Identify the type of function. This is a quadratic function in the form y=a*x2+b*x+c where a=−1 b=0 and c=2 The graph is a parabola opening downward because a<0

2. Determine the vertex. Since b=0 the xcoordinate of the vertex is x=0 Substituting x=0 into the equation gives y=2 The vertex is (0,2)

3. Find the yintercept. Set x=0 to find the yintercept, which is (0,2) This is also the vertex.

4. Find the xintercepts. Set y=0 and solve for x

0=−x2+2

x2=2

x=±√(,2)≈±1.41

5. Plot additional points to define the shape.
   If x=1 y=−(1)2+2=1 Point: (1,1)
   If x=−1 y=−(−1)2+2=1 Point: (−1,1)
   If x=2 y=−(2)2+2=−2 Point: (2,−2)
   If x=−2 y=−(−2)2+2=−2 Point: (−2,−2)

6. Sketch the curve. Draw a smooth, downward-opening parabola passing through the vertex (0,2) and the points (1,1) (−1,1) (2,−2) and (−2,−2)

Final Answer

y=−x2+2

Want more problems? Check here!