Graph y=-x^2

Problem

y=−x2

Solution

1. Identify the type of function, which is a quadratic function in the form y=a*x2+b*x+c

2. Determine the shape of the graph by looking at the leading coefficient a=−1 Since a<0 the parabola opens downward.

3. Find the vertex of the parabola. For y=−x2 the vertex is at the origin (0,0)

4. Calculate additional points to determine the width of the curve.

5. Substitute x=1 into the equation: y=−(1)2=−1 This gives the point (1,−1)

6. Substitute x=2 into the equation: y=−(2)2=−4 This gives the point (2,−4)

7. Reflect these points across the y-axis (the axis of symmetry) to find points (−1,−1) and (−2,−4)

8. Plot the vertex and the calculated points on a coordinate plane and draw a smooth curve connecting them.

Final Answer

The graph of y=−x2 is a downward-opening parabola with its vertex at (0,0)

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