Graph f(x)=-x^2

Problem

ƒ(x)=−x2

Solution

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

2. Determine the vertex by observing that a=−1 b=0 and c=0 The vertex is at (0,0)

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

4. Calculate additional points to determine the width. For x=1 ƒ(1)=−(1)2=−1 For x=2 ƒ(2)=−(2)2=−4

5. Apply symmetry across the y-axis (x=0 to find corresponding points at (−1,−1) and (−2,−4)

6. Sketch the curve through the points (0,0) (1,−1) (−1,−1) (2,−4) and (−2,−4)

Final Answer

ƒ(x)=−x2

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