What does the term 'completing the square' mean?

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form $$(x - p)^2 = q$$ , making it easier to solve for $$x$$ .

What is a factor of a quadratic equation?

A factor of a quadratic equation is an expression that can be multiplied by another expression to yield the original quadratic. For example, in $$2x^2 + 3x - 9$$ , one factor is $$(x + 3)$$ .

How do you determine the reasonable domain for a quadratic function?

The reasonable domain for a quadratic function representing a real-world scenario, like height, is typically restricted to non-negative values, such as $$[0, \, \text{max time}]$$ .

What is exponential growth?

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, often modeled by the function $$p(t) = p_0(1 + r)^t$$ , where $$p_0$$ is the initial amount and $$r$$ is the growth rate.

What is the importance of the initial value in an exponential function?

The initial value in an exponential function represents the starting amount before any growth occurs, which is crucial for understanding the function's behavior over time.

What is the relationship between the roots and the factors of a quadratic?

The roots of a quadratic equation are the values of $$x$$ that make the equation equal to zero, and they correspond to the factors of the quadratic. For example, if $$x = r_1$$ and $$x = r_2$$ are roots, the quadratic can be factored as $$a(x - r_1)(x - r_2)$$ .

What is the process of graphing a quadratic function?

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot these points and draw a smooth curve through them to represent the parabola.

Unit 9-12 District Test Review #2 Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What does it mean for a quadratic to have only one solution?

Back

A quadratic has only one solution when its discriminant is zero. This occurs when the vertex of the parabola touches the x-axis, indicating a repeated root.

3.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex of a quadratic in standard form?

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is the formula for the height of a projectile?

Back

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