Consider the follywing equation. \[ y=x^{2}-3 x-28 \] (a) Use a graphing eitily to graph the equation. Use the graph to acorsximute any \( x \)-ihtercmptc. (Einter ycur ancwers as a camma-separated int: \[ x=\sqrt{\square} \] (b) Set \( y=0 \) and solve the resulting equation. (Enter your answers as a camma separated llst.) \[ x=\square \] (c) Compare the result of part (b) with the \( x \)-intercepts of the grach. The \( x \) values are the same. The \( x \)-values are rediprocals. The \( x \)-values are unrelated.

To understand quadratic equations like the one you're working with, it’s fascinating to note that they have been used for centuries! The ancient Babylonians were solving quadratic equations around 2000 BC, employing geometrical methods long before variables and algebraic notation came into common use. It’s incredible how these foundational techniques have evolved into the algebra we use today! In real life, quadratic equations pop up in various situations. For instance, when throwing a ball, the trajectory follows a parabolic path described by a quadratic equation. This applies to a lot of scenarios in physics, engineering, and even finance when modeling profit margins or calculating optimal pricing strategies. The real-world applications really showcase how essential these equations are in our daily lives!