Question

How is quadratic formula used in everyday life?

Answer 1

Your company is going to make frames as part of a new product they are launching.

The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be `28 cm^2`

The inside of the frame has to be 11 cm by 6 cm

What should the width x of the metal be?

Area of steel before cutting:

Area = `(11 + 2x) × (6 + 2x) cm^2`
Area = `66 + 22x + 12x + 4x^2`
Area = `4x^2 + 34x + 66`
Area of steel after cutting out the 11 × 6 middle:

Area = `+ 34x + 66 - 66`
Area = `4x^2 + 34x`

Let us solve this one graphically!

Here is the graph of 4x2 + 34x :

The desired area of 28 is shown as a horizontal line.

The area equals 28 cm2 when:

x is about -9.3 or 0.8

The negative value of x make no sense, so the answer is:

x = 0.8 cm (approx.)

You can try it out yourself and find the roots of the quadratic equation using the quadratic formula

`x = [ -b ± sqrt(b^2 - 4ac) ] / (2a`

There are many more examples at http://www.mathsisfun.com/algebra/quadratic-equation-real-world.html