What are the solutions of the function $$f(x) = x^2 + 64$$ ?

The solutions are $$-8i$$ and $$8i$$ .

Solve for x: $$-2x^2 + 4x = 9$$

$$x = \frac{2 + i\sqrt{14}}{2}, \frac{2 - i\sqrt{14}}{2}$$ .

What is the standard form of a quadratic equation?

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

What is a real root in a quadratic equation?

A real root is a solution to the quadratic equation that is a real number, occurring when the discriminant is non-negative.

What is the vertex of a quadratic function?

The vertex of a quadratic function $$f(x) = ax^2 + bx + c$$ is the point where the graph changes direction, given by the coordinates $$(-\frac{b}{2a}, f(-\frac{b}{2a}))$$ .

What is the axis of symmetry in a quadratic function?

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

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

Complex Quadratics Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a complex quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the discriminant in a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has two complex solutions (roots) that are conjugates of each other.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What determines if a quadratic will have complex solutions?

Back

The quadratic will have complex solutions if the discriminant is negative.

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