Graph y=-x^2+4

Problem

y=−x2+4

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=4

2. Determine the concavity. Since a=−1 is negative, the parabola opens downward.

3. Find the vertex. The xcoordinate is given by x=(−b)/(2*a) Substituting the values gives x=0/(2*(−1))=0 Substituting x=0 into the original equation gives y=−(0)2+4=4 The vertex is (0,4)

4. Find the yintercept. Set x=0 to find y=4 The yintercept is (0,4) which is also the vertex.

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

0=−x2+4

x2=4

x=±2

The xintercepts are (−2,0) and (2,0)

6. Plot additional points to refine the shape. For x=1 y=−(1)2+4=3 For x=−1 y=−(−1)2+4=3

7. Sketch the curve. Draw a smooth, downward-opening parabola passing through the points (−2,0) (−1,3) (0,4) (1,3) and (2,0)

Final Answer

To graph y=−x2+4 plot the vertex at (0,4) the xintercepts at (−2,0) and (2,0) and draw a downward-opening parabola.

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