Plot the graph of this y = x3 + 4x2 + 2.

Question

y = x3 + 4x2 + 2.

Answer 1

Hi Sosa, the graph of y = x³ + 4x² + 2 is the graph of a cubic function. The graph will cross the x-axis at least once. If we set x = 0, we can get the y-intercept point. The graph crosses the y-axis at the point (0,2), or the y-intercept point. The right side of the curve increases to infinity.

 

The left side of the curve has an stationary point (where the curve stops increasing and starts to decrease) somewhere between -2 and -3 on the x-axis. 

 

Set up a table of values for x and y and then plot the the values.

 

Right side of graph starting at y-intercept point:

 

x-values   0       1       2     ....

 

y-values   2       7       26   .... values continue to increase as x increases

 

Left side of graph starting at the y-intercept point:

 

x-values   0      -1       -2        -3      -4      -5

 

y-values   2        5       10       11       2      -23   .... values continues to decrease as x becomes more negative

 

Note: it appears that y-values increase from -2 to -3 on the x-axis. This is not quite true. There is an stationary point between -2 and -3 on the x-axis. At about -2.6, the y-value reaches its peak and starts to decrease.

 

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