Understanding Quadratic Functions with Complex Zeros

The video tutorial explains how to find a quadratic function with a complex zero of 2i. It highlights that complex zeros come in conjugate pairs, so -2i is also a zero. The tutorial covers how zeros inform the factors of a quadratic function and demonstrates constructing the function using these zeros. It simplifies the function to F(x) = x^2 + 4 and explains that the graph will not intersect the x-axis due to the imaginary nature of the zeros.

What is the form of complex conjugates?

• a + bi and a - bi

• a + b and a - b

• a - b

• a + b

If 2i is a zero of a quadratic function, what must be another zero?

• -2

• 2i

• -2i

• 2

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What do the zeros of a quadratic function tell us about the function?

• The domain of the function

• The y-intercepts

• The factors of the function

• The slope of the function

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What happens graphically if the zeros of a quadratic function are not real?

• The graph will intersect the x-axis

• The graph will be a straight line

• The graph will not intersect the x-axis

• The graph will have a vertex at the origin

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What is the factor form of a quadratic function with zeros 2i and -2i?

• (x - 2)(x + 2)

• (x - 2i)(x + 2i)

• (x + 2i)(x + 2i)

• (x - 2i)(x - 2i)

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

• x^2 + 4

• x^2 - 4

• x^2 + 2

• x^2 - 2

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What is the value of i squared?

• -1

• i

• 1

• 0

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What is the simplified form of the quadratic function with zeros 2i and -2i?

• f(x) = x^2 + 2

• f(x) = x^2 - 4

• f(x) = x^2 - 2

• f(x) = x^2 + 4

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Why does the function f(x) = x^2 + 4 not intersect the x-axis?

• Because it is a linear function

• Because it has complex zeros

• Because it has real zeros

• Because it is a constant function

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What should you remember about the graph of a function with complex zeros?

• It will always intersect the x-axis

• It will have a vertex at the origin

• It will always intersect the y-axis

• It will not intersect the x-axis

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CCSS.HSF-IF.C.7A