What is the axis of symmetry for the quadratic function $$f(x) = a(x - h)^2 + k$$ ?

The axis of symmetry is the vertical line $$x = h$$ .

What are the zeros of the function $$f(x) = x^2 - 4x$$ ?

The zeros are $$x = 0$$ and $$x = 4$$ .

What is the general form of a cubic function with given zeros $$r_1, r_2, r_3$$ ?

The cubic function can be expressed as $$f(x) = a(x - r_1)(x - r_2)(x - r_3)$$ .

How do you determine the vertex of a quadratic function in standard form $$f(x) = ax^2 + bx + c$$ ?

The vertex can be found using $$h = -\frac{b}{2a}$$ and then substituting $$h$$ back into the function to find $$k$$ .

What is the significance of the leading coefficient in a polynomial function?

The leading coefficient determines the end behavior of the graph.

How do you factor the polynomial $$f(x) = 3x^2 + 4x - 4$$ ?

Use the quadratic formula or factoring techniques to find the roots, which are $$x = 0.6666$$ and $$x = -2$$ .

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

Each zero corresponds to a factor of the polynomial in the form $$(x - r)$$ , where $$r$$ is a zero.

What is the standard form of a quadratic function?

The standard form is $$f(x) = ax^2 + bx + c$$ .

How do you find the y-intercept of a polynomial function?

The y-intercept is found by evaluating the function at $$x = 0$$ .

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 the ratio of two polynomials.

What is the importance of the discriminant in quadratic equations?

The discriminant $$D = b^2 - 4ac$$ determines the nature of the roots: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

How do you convert a polynomial from factored form to standard form?

Multiply the factors out to combine like terms.

Chapter 2 Precalculus Assessment Part 1 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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How do you find the zeros of a polynomial function?

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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Find the cubic function with zeros -2, 1, and 3.

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6.

FLASHCARD QUESTION

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What is the vertex form of a quadratic function?

Back

7.

FLASHCARD QUESTION

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