What is the vertex of a parabola given by the quadratic function $$f(x) = ax^2 + bx + c$$ ?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ .

What does the discriminant of a quadratic equation tell us?

The discriminant, given by $$D = b^2 - 4ac$$ , indicates the nature of the roots: D > 0 (two real roots), D = 0 (one real root), D

What is the standard form of a quadratic function?

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

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

Set $$f(x) = 0$$ and solve for x using the quadratic formula $$x = \frac{-b \text{±} \text{√}(b^2 - 4ac)}{2a}$$ .

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

The leading coefficient (a) determines the direction of the parabola: if a > 0, it opens upward; if a

What is the logarithmic function's domain?

The domain of a logarithmic function $$f(x) = \text{log}_b(x)$$ is $$x > 0$$ .

What is the range of the function $$f(x) = \text{log}_b(x)$$ ?

The range is all real numbers, i.e., $$(-\text{∞}, \text{∞})$$ .

What is the relationship between exponential and logarithmic functions?

Logarithmic functions are the inverses of exponential functions. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

What is the base of a logarithm?

The base of a logarithm, denoted as $$b$$ in $$\text{log}_b(x)$$ , is the number that is raised to a power to obtain x.

Algebra Spring semester review 2025 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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Downward

2.

FLASHCARD QUESTION

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x = 1

3.

FLASHCARD QUESTION

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5i√2

4.

FLASHCARD QUESTION

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Left: As x → 1, y → -∞; Right: As x → ∞, y → ∞

5.

FLASHCARD QUESTION

Front

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(1, ∞)

6.

FLASHCARD QUESTION

Front

Define a quadratic function.

Back

7.

FLASHCARD QUESTION

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