Suppose a quadratic function f(x) = x^2 + bx + c has zeros p and q.
a) Let k be an integer. Using only b, c, and k (and x), write a new qudratic function whose zeros are p+k and q+k.
b) Repeat part (a), but write a new function whose zeros are p-k and q-k.
Let k represent a positive integer, so that 2k represents a positive even integer, and suppose we want to answer the following question: How can 2k be given as a sum of two numbers x a nd y so that xy is as large as possible?
a) Answer the question specifically for 2k=10 by trying all possible pairs of integers whose sum is 10. Based on your answer, make a conjecture for the general case.
b. Prove the conjecture you made in part (a) by writing a quadratic function in factored form.
2006-10-12
15:07:17
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4 answers
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asked by
wizard94539
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Mathematics