Solve the quadratic equation: $$x^2 - 5x + 10 = 0$$

The solutions are: $$x = \frac{5 - i\sqrt{15}}{2}$$ and $$x = \frac{5 + i\sqrt{15}}{2}$$ .

What is the simplified form of $$-\sqrt{-8}$$ ?

The simplified form is: $$-2i\sqrt{2}$$ .

Solve the quadratic equation: $$2x^2 + 7x - 15 = 0$$

The solutions are: $$x = -5$$ and $$x = 1.5$$ .

What is the vertex form of a quadratic function?

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

What is the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function given by $$y = ax^2 + bx + c$$ is: $$x = -\frac{b}{2a}$$ .

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

The coefficient 'a' determines the direction of the parabola: if a > 0, the parabola opens upwards; if a

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 given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

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

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x, and factor the resulting perfect square trinomial.

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 $$i = \sqrt{-1}$$ .

How can you graph a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve through them.

What is the importance of the quadratic formula in solving quadratic equations?

The quadratic formula provides a systematic method to find the roots of any quadratic equation, regardless of whether the roots are real or complex.

Solving Quadratics with Complex Solutions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

6.

FLASHCARD QUESTION

Front

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

Back

A quadratic equation has complex solutions if the discriminant is less than zero (D < 0).

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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