real world problem using f(x)=x^2+2 quadratic function

Question

i need to know the real life problem related to this function help me plz.

Answer 1

(note:  If your teacher/book gave an example, you should use that.)

I’m so glad that you are learning “real life problems” in math (that answer the age-old question: “Why do we need to learn this stuff?”)

I observe that f(0) = 2     that’s the y-intercept

As f increases by n units, f(x) increases by n² units.   Now, what does that?  This is called a parabola, and it is used in lots and lots of real-life situations.

My best personal example:  After I’ve squinted at road signs while driving for the last several years, my daughter said, ”Dad, maybe this is the year for glasses.”  So, I went for tests, got a prescription, then bought these curved lenses.  When I look at them from the side and consider that there is a thickness of glass in the center, I also see the curve increasing (and it’s not a circle – I can see that without having my glasses on).  So, I look up eyeglasses on the Internet and find that parabolas are used to make eyeglasses.  They also are used to make telescopes and binoculars.  Wow, optics would be an exciting field if someone understood applications of math.

There are hundred more – find your own.

Also, the formula you find may not be exactly f(x)=x² + 2 but it will resemble it.  (for example, throwing an object into the sky is an upside-down parabola).

Once, I used Gauss’ formula (he was 8 when he discovered it) for the sum of the numbers from 1 to N is N*(N+1)/2    (this is (N2 + N ) / 2, and for very large N, resembles N²).

When teaching computers at college, I bought a “write-home-postcard” in a clear envelope that had a college scene picture on one side and the letter on the other side – but it was a 20-piece puzzle (to read your letter, parents would first have to assemble the puzzle).  I told the class it takes 20 (at most) examines to find a corner (say, upper-left), then 19 examines to find the one that fits to the right of it. Then 18, .., then 1 to finish.  That’s 20+19+18+…+1 to solve the puzzle.  Gauss’ formula says that is 20*21/2 = 210.   With 210 compares, my computer can solve this puzzle.  This puzzle was 4*5, but if it were 8*10, it would take me 80*81/2 = 3240 examines  (note: this is “roughly” increasing as x²).

Well, while looking on the Internet, I found this really weird structure:

      http://www.datapointed.net/2010/09/lewicki-parabola-skate-ramp/