How do you solve the equation $$v^2 + 9 = -19$$ ?

To solve $$v^2 + 9 = -19$$ , first isolate $$v^2$$ : $$v^2 = -19 - 9 = -28$$ . Then, take the square root: $$v = \text{±}i\text{√}{28} = \text{±}2i\text{√}{7}$$ .

What are the roots of the equation $$x^2 + 3x + 2 = 0$$ ?

The roots can be found by factoring: $$(x + 1)(x + 2) = 0$$ , giving roots $$x = -1$$ and $$x = -2$$ .

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 can you determine if a quadratic opens upwards or downwards?

A quadratic opens upwards if $$a > 0$$ and downwards if $$a

What is the axis of symmetry for a quadratic equation?

The axis of symmetry for the quadratic equation $$ax^2 + bx + c = 0$$ is given by the formula $$x = -\frac{b}{2a}$$ .

What is the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation: $$x = \frac{-b \text{±} \text{√}{(b^2 - 4ac)}}{2a}$$ .

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 $$\frac{c}{a}$$ .

What is a complex number?

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 $$i^2 = -1$$ .

How do you convert a quadratic equation to standard form?

To convert a quadratic equation to standard form, rearrange it to the form $$ax^2 + bx + c = 0$$ by moving all terms to one side.

What is the importance of the quadratic equation in real-world applications?

Quadratic equations model various real-world situations, such as projectile motion, area problems, and optimization scenarios.

Quadratics with Complex Numbers Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the discriminant of a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean if the discriminant is less than zero?

Back

3.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the significance of the roots of a quadratic equation?

Back

7.

FLASHCARD QUESTION

Front

What does it mean if the discriminant is equal to zero?

Back

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