Graph y=-x^2+6

Problem

y=−x2+6

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=6 The graph is a parabola that opens downward because a<0

2. Find the vertex of the parabola. Since b=0 the xcoordinate of the vertex is x=(−b)/(2*a)=0 Substituting x=0 into the equation gives y=6 The vertex is (0,6)

3. Determine the yintercept. By setting x=0 we find the yintercept is (0,6) which is also the vertex.

4. Calculate the xintercepts by setting y=0

0=−x2+6

x2=6

x=±√(,6)≈±2.45

5. Plot additional points to define the shape. For x=1 y=−(1)2+6=5 For x=2 y=−(2)2+6=2 Due to symmetry across the yaxis (x=0, the points (−1,5) and (−2,2) are also on the graph.

6. Sketch the curve. Draw a smooth, downward-opening curve passing through the vertex (0,6) the xintercepts (±√(,6),0) and the points (±1,5) and (±2,2)

Final Answer

y=−x2+6

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