Find the negative area of the function
Find the negative area of the function
The function given is . This function represents a parabola opening downwards, with the vertex at . Because is a downward-opening parabola with a vertex below the x-axis at -4, it means every point on the parabola has a y-value less than zero. Thus, for all values of , the function is negative.
The entire graph of this quadratic function lies below the x-axis; therefore, any form of "area" discussed here would necessarily be negative since the function never crosses into positive y-values (it is not asking for the integration under the curve relative to x-axis as such).
Consequently, the situation describes that the parabola completely lies under the x-axis across its domain: for all real .
Therefore, the solution to the problem is: For all , the area is negative.
For all X