Understanding Quadratic Functions with Complex Zeros

The video tutorial explains how to find a quadratic function with a given complex zero, 2 - 3i. It highlights the importance of recognizing complex zeros in conjugate pairs, such as 2 + 3i. The tutorial covers how these zeros relate to the factors of a quadratic function and discusses the implications for graphing, noting that complex zeros do not intersect the x-axis. The video demonstrates the multiplication of complex numbers to derive the quadratic function and simplifies the expression to find one possible function. It concludes with a graphing demonstration and hints at an alternative method using completing the square.

What is the conjugate of the complex zero 2 - 3i?

• 2 - 3i

• 2 + 3i

• -2 + 3i

• -2 - 3i

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CCSS.HSF-IF.C.7C

If a quadratic function has zeros r1 and r2, what is the general form of the function?

• f(x) = a(x + r1)(x + r2)

• f(x) = a(x - r1)(x - r2)

• f(x) = a(x + r1)(x - r2)

• f(x) = a(x - r1)(x + r2)

Tags

CCSS.HSF-IF.C.7A

What happens to the graph of a quadratic function with complex zeros?

• It intersects the x-axis at two points.

• It forms a straight line.

• It does not intersect the x-axis.

• It intersects the x-axis at one point.

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CCSS.HSA.APR.A.1

What is the result of multiplying (x - (2 - 3i))(x - (2 + 3i))?

• x^2 + 4x + 13

• x^2 - 4x - 13

• x^2 + 4x - 13

• x^2 - 4x + 13

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CCSS.HSN.CN.A.1

What is the value of i^2 in complex numbers?

• 1

• -1

• 0

• i

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CCSS.HSN.CN.C.8

What is the sum of the products 2x + 3i and -3i x 2?

• 0

• 6i

• -6i

• 12i

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CCSS.HSN.CN.A.1

What is the simplified form of the expression 4 - 9i^2?

• 4 + 9

• -4 - 9

• 4 - 9

• -4 + 9

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CCSS.HSA.APR.B.3

What is one possible quadratic function with zeros 2 - 3i and 2 + 3i?

• f(x) = x^2 - 4x - 13

• f(x) = x^2 + 4x - 13

• f(x) = x^2 - 4x + 13

• f(x) = x^2 + 4x + 13

What can be added to the quadratic function to change its coefficients but not its zeros?

• A linear term

• A constant factor

• A quadratic term

• A cubic term

What alternative method is mentioned for simplifying the work in finding the quadratic function?

• Completing the square in reverse order

• Using the quadratic formula

• Synthetic division

• Graphical method