Solve by square roots: $$4x^2 - 7 = -40$$ . What are the solutions?

$$x = \\pm \frac{\sqrt{33}i}{2}$$ .

Solve by square roots: $$2x^2 - 2 = -15$$ . What are the solutions?

$$x = \pm \frac{\sqrt{26}i}{2}$$ .

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.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line given by $$x = -\frac{b}{2a}$$ , which divides the parabola into two mirror-image halves.

What is the significance of the leading coefficient in a quadratic equation?

The leading coefficient (the value of $$a$$ in $$ax^2 + bx + c$$ ) determines the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a

How can you determine if a quadratic equation can be factored?

A quadratic equation can be factored if its discriminant is a perfect square, indicating that the roots are rational.

What is the relationship between the roots and the coefficients 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 $$\frac{c}{a}$$ .

Quadratic Equations with Complex Solutions Practice Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define a quadratic equation.

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What does it mean for a quadratic equation to have complex solutions?

Back

4.

FLASHCARD QUESTION

Front

How do you find the roots of a quadratic equation using the square root method?

Back

5.

FLASHCARD QUESTION

Front

What is the discriminant of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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