Question - Solving a Cubic Equation with a Given Value of x
Solution:
The image shows two equations:1) $$ y = x^3 + 3x^2 - 24x + b $$2) $$ x_0 = 2 $$It appears that you have been provided with a cubic equation and a value for $$ x_0 $$, which typically would suggest either finding the value of y when $$ x = x_0 $$, or determining a constant in the equation, like 'b', based on some additional information about $$ x_0 $$. However, the context or the specific question you need to solve with these equations is not given. If the problem is to find the corresponding y-value (let's call it $$ y_0 $$) when $$ x = x_0 $$, then we would substitute $$ x = 2 $$ into the first equation:$$ y_0 = (2)^3 + 3(2)^2 - 24(2) + b $$$$ y_0 = 8 + 3(4) - 48 + b $$$$ y_0 = 8 + 12 - 48 + b $$$$ y_0 = 20 - 48 + b $$$$ y_0 = -28 + b $$So the $$ y_0 $$ value when $$ x = 2 $$ depends on the value of 'b'.However, if b is what you're supposed to find, then there is missing information. There needs to be additional information about the graph or a specific y-value when $$ x = x_0 $$ to find 'b'. If that's the case, please provide the additional information so I can assist further.
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