Questions: Graph y=-x^3-3x^2

Graph y=-x^3-3x^2
Transcript text: Graph $y=-x^{3}-3 x^{2}$
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Solution

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Solution Steps

Step 1: Identify the function to be graphed

The function given is \( y = -x^3 - 3x^2 \).

Step 2: Determine the range for the graph

To graph the function, we need to determine a suitable range for \( x \) and \( y \). A typical range for \( x \) might be from -3 to 3, and for \( y \), we can calculate the values at these extremes to determine a suitable range.

Step 3: Calculate the range for \( y \)
  • At \( x = -3 \), \( y = -(-3)^3 - 3(-3)^2 = 27 - 27 = 0 \).
  • At \( x = 3 \), \( y = -(3)^3 - 3(3)^2 = -27 - 27 = -54 \).

Thus, a suitable range for \( y \) might be from -60 to 10.

Final Answer

The function to be graphed is \( y = -x^3 - 3x^2 \) with a range for \( x \) from -3 to 3 and for \( y \) from -60 to 10.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -60, "ymax": 10}, "commands": ["y = -x3 - 3*x2"], "latex_expressions": ["$y = -x^3 - 3x^2$"]}

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