What Is A Real Life Example Of A Quadratic Equation And Please Show Work?

The general form of a quadratic equation is ax² + bx + c = 0 with x as a variable and a, b and c are constants. The quadratic equation can be applied to many real life examples including finding the stopping distance of a car or how to kick a perfect drop goal in a rugby match.

Working out trajectories in projectile motion, or to put it more simply relating time to distance, is used in the science of ballistics, which examines the effect of gravity on moving objects.

Using the quadratic formula which relates time to distance it is possible to work out exactly which angle to kick a rugby ball in order to score the perfect drop goal. You must work out the angle and the velocity correctly so that when it goes a distance (x) to the goal it is at the correct height (y) for it accurately clear the post.

So to take it from the beginning, the ball falls in the direction (y) with a steady acceleration (g). It travels straight in the (x) direction at a constant velocity. So if the ball starts at x = y = 0 with velocity (u) in the (x) direction and travels upwards at velocity (v) then you will be able to work out the position of the ball at time (t) by: X = ut and y = vt - 1/2gt².

This is known as a parabolic equation and is also used by the army for missile calculations. For more real life examples and explanations of quadratic equations check out the ‘101 uses of a quadratic equation’ at: plus.maths.org/content/os/issue29/features/quadratic/index

Y = P(1-2x-x^2)

P represents the cost of a Product
x represents the percentage off

Y = P(1-x)(1-x)

let P = $250 (cost of the product)
let x have two values  {40%,10%}

A shoe store has a sale on designer shoes,
the original price is $250. All shoes are 40% off,
but today only you can take an additional 10% 0ff.

By using Y(the new price after deductions)
convert 40% and 10% to decimals

0.40, and 0.10

Y = $250(1-0.40)(1-0.90)
   = $250(0.6)(0.90) = $135

The new price is $135

It is common for people to add the percentages and get 50% off.
But with the equation used  the percentage off is 1- (0.6)(0.9) = 46%.

Is this a good example.

Pythagorean Theorem is a real life example of quadratic equation red the example on thislink and you will understand everything!
there are other examples too like spring-damper system link
 

How far a bullet flies. How long it will take you to hit the ground if you jump off of a cliff. How high a ball bounces. These are probably the simplest to conceptualize.