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# based on zeros how can you determine what it's graphed function is?

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when a quadratic equation is graphed how am i supposed to determine what the equation itself is when only the zeros of the function are given?

Guest Apr 8, 2015

#2
+26642
+10

With a quadratic equation there are always two roots (though one might be repeated), so, if x1 and x2 are the roots, then the equation could be expressed as y = (x - x1)*(x - x2)  or y = -(x - x1)*(x - x2).  You would need extra information to determine which of these two it is (one is concave up, the other is concave down).

Alan  Apr 8, 2015
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#1
+85958
+10

Sometimes, this is difficult....for instance, let's suppose that someone told you the zeroes of a function were 0 and 2

Have a look at this graph......https://www.desmos.com/calculator/elxkpygjkn

Notice that both functions have the same zeroes - 0 and 2 - but the the"blue" function has a zero of 2 with a multiplicity of 2.....thus, we need to know not only the zeroes, but what  multiplicity is associated with each one to be able to determine the equation and draw the proper graph......!!!!

Also...remember that some functions may not have any "real" zeroes at all!!!

CPhill  Apr 8, 2015
#2
+26642
+10

With a quadratic equation there are always two roots (though one might be repeated), so, if x1 and x2 are the roots, then the equation could be expressed as y = (x - x1)*(x - x2)  or y = -(x - x1)*(x - x2).  You would need extra information to determine which of these two it is (one is concave up, the other is concave down).

Alan  Apr 8, 2015
#3
+92254
+5

I wrote this post a while back it is on interpreting polynomial graphs (you can use it in reverse too)

It is packed full of VERY useful information.

If you digest what I am saying it will go well for you :)

http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed

Melody  Apr 8, 2015
#4
+889
+5

Given that it's a quadratic with zeros x1 and x2, the best that you can do is to say that the equation is

y = k(x - x1)(x - x2), where k is some non-zero constant, positive or negative.  If k is positive the graph will be concave up, if negative it will be concave down. You have an infinite number of possibilities.

Bertie  Apr 8, 2015

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