a) \( y=x^{2}-7 x \) б) \( y=-3 x^{2}-13 x \)
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The Deep Dive
Did you know that the equations you've presented are quadratic functions? Quadratics have a fascinating history dating back to the ancient Babylonians, who solved equations like these using geometric methods. They also laid the groundwork for algebra as we know it today! These quadratic equations represent parabolas when graphed. For real-world applications, you might see their forms in physics, such as tracking the path of a ball thrown in the air or even in optimizing profit and loss scenarios in economics. So, the next time you see a curve, think about how it could relate to the real world!