document.write( "Question 143398: What are some examples of word problems from day to day life that can be translated to quadratic equations? \n" ); document.write( "

Algebra.Com's Answer #104420 by nabla(475) $\"\"$ $\"About$

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I'm going to give you the first example that comes to mind:\r
\n" ); document.write( "\n" ); document.write( "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. \r
\n" ); document.write( "\n" ); document.write( "Let's make an equation for this. \r
\n" ); document.write( "\n" ); document.write( "a=a(x)=x; This is your acceleration at time x.\r
\n" ); document.write( "\n" ); document.write( "If we integrate this function we come up with a different formula:\r
\n" ); document.write( "\n" ); document.write( " $\"int%28+x%2C+dx+%29=%281%2F2%29%28x%5E2%29%2Bc\"$ . 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.\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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