Question 143398: What are some examples of word problems from day to day life that can be translated to quadratic equations? Answer by nabla(475) (Show Source):
You can put this solution on YOUR website! I'm going to give you the first example that comes to mind:
Say you are driving down the road and the speed limit changes to +10 mph so you accelerate in order to approach the speed limit.
Let's make an equation for this.
a=a(x)=x; This is your acceleration at time x.
If we integrate this function we come up with a different formula:
. This gives you the velocity, per some constant c, of the acceleration function. We can continue to integrate and get the position function of the vehicle. I will omit this, simply because I've already put too much calculus into this answer.
As you can see, however, given a directly varied acceleration (that is, the acceleration is the same as the time), we end up with a function to describe the velocity of the vehicle that is a quadratic equation with a=1/2 b=0 and c a constant.
Let's do an example. Say you want to know what your acceleration is at x=5. According to the formula, f(5)=5 implies that the velocity will be 25/2+c mph. The constant is of course the speed at which you were traveling before accelerating. In any case, this certainly applies to many peoples' day to day lives.
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