Solving a Cubic Equation with a Given Value of x
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.
