What does it mean if the discriminant (b^2 - 4ac) is positive, zero, or negative?

If the discriminant is positive, there are two distinct real solutions. If it is zero, there is one real solution (a repeated root). If it is negative, there are two complex solutions.

Solve by completing the square: $$k^2 - 12k + 23 = 0$$

$$k = 6 \text{±} \text{sqrt}(13)$$ .

Solve the quadratic equation by completing the square: $$x^2 + 4x - 35 = 5$$

$$x = 1 \text{±} \text{sqrt}(40)$$ or $$x = 1 \text{±} 2\text{sqrt}(10)$$ .

Solve by completing the square: $$x^2 + 12x = 5$$

$$x = -6 \text{±} \text{sqrt}(41)$$ .

What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How do you convert a quadratic equation from standard form to vertex form?

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form, complete the square on the quadratic expression.

What is the significance of the imaginary unit 'i'?

The imaginary unit 'i' is defined as $$i = \text{sqrt}(-1)$$ and is used to extend the real number system to include solutions to equations that do not have real solutions.

What is the relationship between complex numbers and the Cartesian plane?

Complex numbers can be represented as points in the Cartesian plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

Completing the Square and Complex Numbers Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the process to complete the square for a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What do you do to the 'b' value to correctly complete the square?

Back

Divide it by 2 and square the result.

3.

FLASHCARD QUESTION

Front

What is a complex number?

Back

4.

FLASHCARD QUESTION

Front

How do you add two complex numbers?

Back

5.

FLASHCARD QUESTION

Front

What is the conjugate of a complex number?

Back

6.

FLASHCARD QUESTION

Front

How do you multiply two complex numbers?

Back

7.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

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