Complete the sentence below. The function \( f(x)=x^{2} \) is decreasing on the interval The function \( f(x)=x^{2} \) is decreasing on the interval

The function \( f(x)=x^{2} \) is decreasing on the interval \((-∞, 0)\). Here, as you move from left to right, the values of \( f(x) \) decrease until they reach the vertex at \( x=0 \), where the function then starts to increase as you move into the positive realm. Quadratic functions can often be graphed, and understanding their behavior leads to fascinating applications in areas like physics and economics! For instance, in projectile motion, the path of a ball thrown into the air follows a parabolic trajectory described by a function similar to \( f(x) \). This means that the concept of rising and falling is captured beautifully by the same function that defines its shape!