Write a quadratic function h whose zeros are 2 and 7.​

One way to create a function from two zeros is to essentially work backward from the position where we're normally asked to begin.

The step before discovering what the zeros are is to look at the two binomial terms that we create after factoring the trinomial we're normally given.

We have many, many factors that would create zeros of 5 and 7, so let's try an easy choice.

Since we know the X of one term is 5, what operation(s) could we perform to make that five into a zero? Well, we can just subtract five.

So there's our first term: (X-5)

We do the same to the 7 with the other term. Once we subtract 7 from that, we have a zero there as well.

Our two binomials are (X-5)(X-7)  

If we FOIL those two terms [x*x = x2; x*-7 = -7x; x*-5 = -5x; -5*-7 = 35] and combine the like terms, we're left with one of many quadratic functions in which the zeros are 5 & 7:  

x2-12x+35

Step-by-step explanation:

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step-by-step explanation: