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Write a quadratic function f whose zeros are 7 and -5.

Write a quadratic function f whose zeros are 7 and -5.-example-1
User Toam
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1 Answer

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Answer:

f(x) = x² -2x -35

Explanation:

You want a quadratic function that has zeros 7 and -5.

Factors

Each zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).

f(x) = (x -7)(x +5)

f(x) = x² -2x -35

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Additional comment

You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.

sum: 7-5 = 2

product: (7)(-5) = -35

quadratic: f(x) = x² -2x -35

User Sunny Sunny
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