What is the factorization of the polynomial $$8x^3 + 125$$ ?

The correct factorization is $$(2x + 5)(4x^2 - 10x + 25)$$ .

Simplify the expression $$(4 - 3i)(2 + 5i)$$ .

The simplified form is $$23 + 14i$$ .

What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \textpm \textsqrt{b^2 - 4ac}}{2a}$$ , used to find the roots of the quadratic equation $$ax^2 + bx + c = 0$$ .

What is the vertex form of a quadratic function?

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

What is the definition of a function?

A function is a relation that assigns exactly one output for each input from its domain.

What is the difference between a linear function and a quadratic function?

A linear function has the form $$f(x) = mx + b$$ and graphs as a straight line, while a quadratic function has the form $$f(x) = ax^2 + bx + c$$ and graphs as a parabola.

What does it mean for a function to be one-to-one?

A function is one-to-one if it never assigns the same value to two different domain elements.

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

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

What is an asymptote?

An asymptote is a line that a graph approaches but never touches or intersects.

What is the difference between domain and range?

The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values).

Algebra II Midterm Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.C.4

2.

FLASHCARD QUESTION

Front

Back

There is no solution because the absolute value cannot be negative.

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSN.CN.C.8

4.

FLASHCARD QUESTION

Front

What is a characteristic of the cube root parent function's graph?

Back

The graph has a y-intercept at the origin, includes all real numbers in domain and range, and has no distinct max or min point.

Tags

CCSS.HSF-IF.C.7B

5.

FLASHCARD QUESTION

Front

What is the range of the function if the output is limited to values between -3 and 3?

Back

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

6.

FLASHCARD QUESTION

Front

Define a polynomial function.

Back

7.

FLASHCARD QUESTION

Front

What is the difference between a rational and an irrational number?

Back

Tags

CCSS.8.NS.A.1

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