Solve for x: $$x^2 + 4 = 0$$

The solutions are $$x = 2i$$ and $$x = -2i$$ .

How can you convert a quadratic equation from standard form to vertex form?

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form, complete the square.

What is the significance of the vertex in a quadratic function?

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Solve for x: $$x^2 - 6x + 10 = 0$$

The solutions are $$x = 3 - i\sqrt{1}$$ and $$x = 3 + i\sqrt{1}$$ .

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 formula $$x = -\frac{b}{2a}$$ .

How do you find the x-intercepts of a quadratic function?

The x-intercepts can be found by solving the equation $$ax^2 + bx + c = 0$$ using the quadratic formula.

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

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

Solve for x: $$2x^2 + 8 = 0$$

The solutions are $$x = -2i$$ and $$x = 2i$$ .

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.

Solving quadratics with Complex solutions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have two real solutions, one real solution (a repeated root), or two complex solutions.

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

Tags

CCSS.HSA-REI.B.4B

5.

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

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

7.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

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