What is the first step in solving the equation $$x^2 + 6x - 13 = 3$$ ?

Subtract 3 from both sides to set the equation to zero: $$x^2 + 6x - 16 = 0$$ .

Solve the equation $$2x^2 + 4x + 10 = 0$$ using the Quadratic Formula.

The solutions are $$x = -1 \\pm 2i$$ .

How do you apply the Quadratic Formula to the equation $$-12q^2 + 3q + 7 = 0$$ ?

Identify coefficients: a = -12, b = 3, c = 7. Then plug into the formula: $$q = \frac{-3 \\pm \\sqrt{3^2 - 4(-12)(7)}}{2(-12)}$$ .

What is the result of $$6^2 - 4(1)(-16)$$ ?

The result is $$36 + 64 = 100$$ , which is positive, indicating two real solutions.

What does it mean to 'simplify' answers in the context of quadratic equations?

Simplifying answers involves reducing fractions, combining like terms, and expressing complex numbers in standard form.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants.

What is the role of the coefficients a, b, and c in the Quadratic Formula?

The coefficients a, b, and c represent the numerical values in the quadratic equation $$ax^2 + bx + c = 0$$ , which are used to calculate the roots.

How can you check if your solutions to a quadratic equation are correct?

Substitute the solutions back into the original equation to see if they satisfy it.

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

The roots of a quadratic equation correspond to the x-intercepts of its graph, which is a parabola.

What is the vertex of a parabola represented by a quadratic equation?

The vertex is the highest or lowest point of the parabola, found using the formula $$x = -\frac{b}{2a}$$ .

Quadratic Formula with Complex Solutions Warmup 2 Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

2.

FLASHCARD QUESTION

Front

What does it mean if a quadratic equation has complex solutions?

Back

Complex solutions occur when the discriminant (the part under the square root in the Quadratic Formula) is negative, indicating that the solutions involve imaginary numbers.

3.

FLASHCARD QUESTION

Front

What is the discriminant in the Quadratic Formula?

Back

4.

FLASHCARD QUESTION

Front

How do you determine if a quadratic equation has real or complex solutions?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the 'i' in complex solutions?

Back

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