What is the imaginary unit $$i$$ ?

The imaginary unit $$i$$ is defined as $$i = \sqrt{-1}$$ . It is used to express complex numbers and allows for the solution of equations that do not have real solutions.

How do you simplify the square root of a negative number?

To simplify the square root of a negative number, factor out -1. For example, $$\sqrt{-x} = i\sqrt{x}$$ .

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root, given by $$D = b^2 - 4ac$$ . It determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D

How do you write a quadratic equation given three points?

To write a quadratic equation given three points, use the general form $$y = ax^2 + bx + c$$ . Substitute the x and y values of the points into the equation to create a system of equations, then solve for a, b, and c.

What is the process to convert a complex number to standard form?

To convert a complex number to standard form, ensure it is expressed as $$a + bi$$ . For example, if given $$-6 - 14i$$ , it is already in standard form.

What is the result of multiplying two imaginary numbers?

When multiplying two imaginary numbers, such as $$(-7i)(-9i)$$ , the result is a real number. For example, $$(-7i)(-9i) = 63$$ because $$i^2 = -1$$ .

A parabola is a U-shaped curve that represents the graph of a quadratic function. It can open upwards or downwards depending on the sign of the coefficient $$a$$ in the equation $$y = ax^2 + bx + c$$ .

How do you identify the axis of symmetry of a parabola?

The axis of symmetry of a parabola given by the equation $$y = ax^2 + bx + c$$ is the vertical line $$x = -\frac{b}{2a}$$ .

What is the significance of the vertex in a parabola?

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the quadratic function.

A2.Fall Final 2024 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

2.

FLASHCARD QUESTION

Front

How do you solve a quadratic equation using the quadratic formula?

Back

3.

FLASHCARD QUESTION

Front

What is a complex number?

Back

4.

FLASHCARD QUESTION

Front

How do you multiply two complex numbers?

Back

5.

FLASHCARD QUESTION

Front

What is the standard form of a parabola?

Back

6.

FLASHCARD QUESTION

Front

How do you find the vertex of a parabola given in standard form?

Back

7.

FLASHCARD QUESTION

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Back

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