Graph -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 vertex by observing that b=0 and c=0 which places the vertex at the origin (0,0)

3. Analyze the leading coefficient a=−1 Since a is negative, the parabola opens downward.

4. Calculate several points to determine the shape of the curve.

5. Substitute x=1 to get y=−(1)2=−1 giving the point (1,−1)

6. Substitute x=2 to get y=−(2)2=−4 giving the point (2,−4)

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

8. Plot the points and draw a smooth, downward-opening curve through them.

Final Answer

y=−x2

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