Solve the equation $$-x^2 + 6x - 10 = 0$$ using the Quadratic Formula.

The solutions are $$3 \pm i$$ .

Identify the leading coefficient in the quadratic equation $$y = x^2 + 5x + 7$$ .

The leading coefficient is $$1$$ .

What is the leading coefficient in the equation $$y = -x^2 - 5x + 12$$ ?

The leading coefficient is $$-1$$ .

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 that divides the parabola into two mirror-image halves. It can be found using the formula $$x = -\frac{b}{2a}$$ .

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

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It represents the maximum or minimum value of the function.

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

The x-intercepts can be found by setting $$y = 0$$ and solving the quadratic equation using the Quadratic Formula.

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

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

By calculating the discriminant $$b^2 - 4ac$$ . If it is negative, the roots are complex; if it is zero or positive, the roots are real.

Quadratic Formula with Complex Roots Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

2.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What are complex roots?

Back

Complex roots are solutions to polynomial equations that include imaginary numbers. They occur when the discriminant of a quadratic equation is negative.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

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