(g) \( y=x^{2}-4 \)

Did you know that the equation \( y = x^2 - 4 \) is a classic example of a quadratic function? Quadratics have a "U" shaped graph called a parabola. This specific function opens upwards and its vertex, the lowest point of the graph, is located at (0, -4). You can easily sketch the graph by plotting a few key points, such as (-2, 0) and (2, 0)—these are your x-intercepts where the graph crosses the x-axis! Now, how can we use this quadratic in the real world? Quadratics often model scenarios involving projectile motion, such as determining the height of an object thrown in the air. If you think of this graph as a path of a ball thrown from a height of 4 units above the ground, you can see how it rises, reaches its peak, and then falls back down—illustrating both the beauty and practicality of parabolas!