# How is quadratic formula used in everyday life?

Jan 14, 2015

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 $28 c {m}^{2}$

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 = $66 + 22 x + 12 x + 4 {x}^{2}$
Area = $4 {x}^{2} + 34 x + 66$
Area of steel after cutting out the 11 × 6 middle:

Area = $+ 34 x + 66 - 66$
Area = $4 {x}^{2} + 34 x$

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