Question

1. approximate when the function ( y = x ^ { 2 } - 3 x - 4 ) is decreasing.

Explanation:

Step1: Find the vertex of the parabola

For a quadratic function \(y = ax^{2}+bx + c\), the \(x\) - coordinate of the vertex is given by \(x=-\frac{b}{2a}\). In the function \(y=x^{2}-3x - 4\), \(a = 1\), \(b=-3\). So \(x=\frac{3}{2}=1.5\).

Step2: Determine the interval of decrease

Since \(a = 1>0\), the parabola opens upwards. A parabola \(y = ax^{2}+bx + c(a>0)\) is decreasing on the interval \((-\infty,-\frac{b}{2a})\).

Answer:

The function \(y=x^{2}-3x - 4\) is decreasing for \(x<1.5\) (or \(x < \frac{3}{2}\))