It comes up in nearly every single math class. Somebody will ask their algebra teacher, in the throes of a lecture on solving quadratic equations or graphing lines, "when will I ever use this?" or "I'm going to be a [fill in the blank]--how will knowing
this stuff help me?"
I have a friend, recently departed from this life, who taught mathematics at a community college. He once posted on Facebook that his standard answer to such queries was that students were not in school to be trained, but to be educated. There is a difference. If you are in a technical school for a job consisting of specific tasks that don't require higher mathematics, then fine, you don't need to be taught Descartes' rule of signs or the Pythagorean theorem. Your choice, your loss.
But odds are, you are not in public high school, or going to college, to be trained. You are seeking an education. You are looking to gain a foothold in the common intellect of civilized man. A significant part of that goal is to get a sense of the view afforded through the lens of mathematics.
"Why do I need to know this?" It is one of the most frustrating questions to ask a math teacher, actually, because the answer is so vast, and so subtle, that it defies human language to compress into a sound bite short enough to fit into the modern attention span.
1. It's so that you stoopid do sownd not liek u r. The world is full of smart people--including and especially those from whom you will eventually be seeking employment. Hold your own in a conversation with an educated citizen, whether verbally or in writing, and you will gain much-needed respect. Language = respect = job = money = ability to live after the manner of your choosing. As a corollary, the greater the circle of your education, the more of the world's literature and thinking you will be able to comprehend on your own, and perhaps even contribute your own small portion.
2. It's so that you can reason your way through problems you encounter in life. The mere exercise of having struggled with a "hard" subject strengthens your mind and gives you the confidence you need in tackling issues that may or may not require you to write a onomatopoetic expression or to calculate the area under a logarithmic curve.
3. Mathematical ideas and skills have a way of cropping up when you least expect them. The more you know math and physics (pardon the plug for my specialties), the more readily you will recognize when principles of those topics are in play--and once recognized and recalled, awareness of the same gives you a huge advantage in making a decision.
I'm sure there is much more to be said on this topic, but that is all for now. Go learn something today, whether or not it fits in your vocational goals!
At your service,