Arc De Triomphe

     Now that you know all about parabolas and quadratic equations, you can apply them to real life situations and problems. People use parabolas and their formulas to solve things such as the arc of a ball, or the shape of a spout of water.

     For example, say there is a basketball player trying to improve his shot. The current equation for his shot is f(x)=-3x^2+6x+10. He realizes the equation for the perfect shot is f(x)=-x^2 +4x. As a quadratic equation, by how much does he have to change his shot?

     To solve the problem above, you subtract the two equations. (-3x^2+6x+10) - (-x^2+4x). First, you distribute the negative sign into the second polynomial, making it (-3x^2+6x+10) + (x^2-4x). Then you combine the like terms. -3x^2 + x^2 is equal to -2x^2. 6x-4x is 2x. 10+0 equals 10. Then you rewrite the equation. The equation showing how much he should change his shot is f(x)= -2x^2 + 2x + 10.

     Another problem that we can use is a fotball player's punt. If he knows he needs to adjust his punt by 3x^2+3x+4, and this will result in a punt of -2x^2+5x+6, what is his current punt arc? To solve, you subtract the equations. (-2x^2+5x+6) - (3x^2+3x+4). Distribute the negative sign: (-3x^2-3x-4.) Then you combine like terms. -2x^2 - 3x^2 is equal to -5x^2.  5x - 3x is 2x. 6 - 4 equals 2. So if you rewrite it, you find his current punt is -5x^2 + 2x + 2.