Calculate Negative Area of f(x)=-x²: Quadratic Function Analysis

Video Solution

Solution Steps

00:00 Find the negative domain of the function

00:03 Notice the coefficient of X squared is negative, so the function is concave down

00:08 The negative domain is actually below the X-axis

00:12 Therefore, substitute Y=0 to find the intersection points with the X-axis

00:18 This is the intersection point of the function with the X-axis

00:25 Let's mark the intersection points with the X-axis

00:30 The negative domain is below the X-axis

00:39 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Understand that the function $f(x) = -x^2$ describes a downward-facing parabola with its vertex at the origin (0,0).
Step 2: Analyze where the function has negative values. For $f(x) = -x^2$ , any value of $x \neq 0$ will yield negative output since squaring any nonzero value is positive and multiplying by $-1$ gives a negative result.
Step 3: Recognize that the point $x = 0$ results in $f(0) = 0$ , meaning exactly at the vertex there is no negative value.

From these observations, you can conclude that $f(x)$ is negative for all $x \neq 0$ .

Therefore, the solution to the problem is $x \neq 0$ .