Calculate Negative Area: Finding Area Below y=-(x+3)²-4

Question

Find the negative area of the function

y=(x+3)24 y=-(x+3)^2-4

Video Solution

Step-by-Step Solution

The function given is y=(x+3)24 y = -(x+3)^2 - 4 . This function represents a parabola opening downwards, with the vertex at (3,4) (-3, -4) . Because y=(x+3)24 y = -(x+3)^2 - 4 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 x x , 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 x x .

Therefore, the solution to the problem is: For all x x , the area is negative.

Answer

For all X