Writing Polynomial Functions from Zeros

The video tutorial explains how to write polynomial functions given their zeros. It covers the concept of zeros as X intercepts and demonstrates how to express them as factors of the polynomial. The tutorial includes examples with both real and imaginary zeros, showing the process of multiplying factors to form the polynomial function. It emphasizes the importance of writing the final polynomial in standard form.

What is a zero of a polynomial function?

• A point where the function has a minimum value

• A point where the function crosses the y-axis

• A point where the function has a maximum value

• A point where the function crosses the x-axis

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CCSS.HSF-IF.C.7C

If 2 is a zero of a polynomial function, what is the corresponding factor?

• x - 2

• x^2 + 2

• x + 2

• x^2 - 2

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CCSS.HSF-IF.C.7C

What happens when you multiply conjugate pairs like (x - 3) and (x + 3)?

• You get a cubic term

• You get a constant term

• You get a linear term

• You get a quadratic term with no middle term

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CCSS.HSA.APR.A.1

What is the polynomial function with zeros 4, 3, and -3?

• x^3 - 4x^2 + 9x - 36

• x^3 + 4x^2 - 9x - 36

• x^3 + 4x^2 + 9x + 36

• x^3 - 4x^2 - 9x + 36

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CCSS.HSA.APR.B.3

If 7i is a zero of a polynomial function, what must also be a zero?

• -7

• 7i

• 7

• -7i

What is the result of multiplying (x - 7i) and (x + 7i)?

• x^2 - 14i

• x^2 + 14i

• x^2 + 49

• x^2 - 49

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CCSS.HSA.APR.A.1

What is the polynomial function with zeros 2, 7i, and -7i?

• x^3 + 2x^2 + 49x - 98

• x^3 - 2x^2 + 49x - 98

• x^3 + 2x^2 - 49x + 98

• x^3 - 2x^2 - 49x + 98

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CCSS.HSA.APR.B.3

What is the standard form of a polynomial function?

• In any order

• With all terms having the same exponent

• From the lowest exponent to the highest exponent

• From the highest exponent to the lowest exponent

What is the value of i^2?

• i

• 1

• 0

• -1

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CCSS.HSN.CN.A.1

Why do imaginary zeros always come in pairs?

• Because they are always negative

• Because they are real numbers

• Because they are always positive

• Because they are conjugates

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CCSS.HSN.CN.C.9