How do you simplify $$\text{sqrt}(-125)$$ ?

$$\text{sqrt}(-125) = 5\text{sqrt}(5)i$$ .

Solve the equation $$x^2 - 6x + 4 = 0$$ using the quadratic formula.

The solutions are $$x = 3 \text{pm} \text{sqrt}(5)$$ .

What are the roots of the equation $$x^2 + 2x - 24 = 0$$ ?

The roots are $$x = -6$$ and $$x = 4$$ .

What is the standard form of a quadratic function?

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

What is the vertex of a quadratic function?

The vertex of a quadratic function in standard form $$f(x) = ax^2 + bx + c$$ is given by the point $$\text{V} = igg(-\frac{b}{2a}, figg(-\frac{b}{2a}igg)igg)$$ .

What is the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function $$f(x) = ax^2 + bx + c$$ is the vertical line $$x = -\frac{b}{2a}$$ .

What does it mean for a quadratic function to have complex roots?

A quadratic function has complex roots when its discriminant is negative, indicating that the graph does not intersect the x-axis.

What is the relationship between the coefficients and the roots of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

How do you determine the number of real roots of a quadratic equation?

You determine the number of real roots by calculating the discriminant $$b^2 - 4ac$$ . If it is positive, there are 2 real roots; if zero, 1 real root; if negative, no real roots.

Complex Numbers and Quadratic Functions Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

2.

FLASHCARD QUESTION

Front

What is the imaginary unit 'i'?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic function indicate?

Back

5.

FLASHCARD QUESTION

Front

If a quadratic function has a discriminant of 4, how many x-intercepts does it have?

Back

It has 2 x-intercepts.

6.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

7.

FLASHCARD QUESTION

Front

Back

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