What is the quadratic formula?

The quadratic formula is used to find the solutions of a quadratic equation of the form $$ax^2 + bx + c = 0$$ . It is given by $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ .

What is the difference between a polynomial and a rational function?

A polynomial is a function that consists of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials. For example, $$f(x) = \frac{{p(x)}}{{q(x)}}$$ where both $$p(x)$$ and $$q(x)$$ are polynomials.

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots of a quadratic equation. If $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; and if $$D

How do you determine the end behavior of a polynomial function?

The end behavior of a polynomial function is determined by its leading term. If the leading coefficient is positive and the degree is even, the ends rise; if negative, the ends fall. If the degree is odd, one end rises and the other falls.

What is the relationship between the zeros of a polynomial and its factors?

The zeros of a polynomial correspond to the values of $$x$$ that make the polynomial equal to zero. Each zero $$r$$ corresponds to a factor of the form $$(x - r)$$ .

What is a complex zero?

A complex zero is a solution to a polynomial equation that is not a real number. Complex zeros occur in conjugate pairs, meaning if $$a + bi$$ is a zero, then $$a - bi$$ is also a zero.

How do you find the vertical asymptotes of a rational function?

To find the vertical asymptotes of a rational function, set the denominator equal to zero and solve for $$x$$ . The values of $$x$$ that make the denominator zero are the vertical asymptotes.

What is the process for factoring a polynomial?

Factoring a polynomial involves expressing it as a product of its factors. This can be done by finding common factors, using the difference of squares, or applying the quadratic formula for quadratics.

Review for NC Math 3 EOC Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What does it mean for a zero to have multiplicity?

Back

3.

FLASHCARD QUESTION

Front

How do you find the lead coefficient of a polynomial?

Back

4.

FLASHCARD QUESTION

Front

What is function composition?

Back

5.

FLASHCARD QUESTION

Front

How do you solve an absolute value equation?

Back

6.

FLASHCARD QUESTION

Front

What is a vertical asymptote?

Back

7.

FLASHCARD QUESTION

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable. This can involve factoring, using the quadratic formula, or synthetic division.

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