Questions and Answers
What is a quadratic function?
Define a parabola.
U-shaped curve
What is the axis of symmetry in relation to a parabola?
The line through the vertex that divides the parabola into two congruent halves.
What is the standard form of a quadratic function?
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What is the minimum value of a parabola when it opens upward?
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What is the maximum value of a parabola when it opens downward?
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What is a zero of a function?
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What are the roots of an equation?
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Define binomials.
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Define trinomials.
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What does completing the square involve?
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What is the imaginary unit?
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Define the vertex of a parabola.
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What is the vertex form of a quadratic function?
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What is an imaginary number?
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Define a complex number.
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What is the real part of a complex number?
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What is the imaginary part of a complex number?
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Define a complex conjugate.
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What is a quadratic inequality in two variables?
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What is the absolute value of a complex number?
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Define the complex plane.
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What is the discriminant in relation to the quadratic formula?
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What is quadratic regression?
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What is a quadratic model?
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Study Notes
Quadratic Functions and Properties
- A quadratic function is represented as f(x) = a(x - h)² + k, where a ≠ 0.
- The parabola is the graph of a quadratic function, characterized by its U-shape.
Key Features of Parabolas
- The axis of symmetry is a vertical line that runs through the vertex, dividing the parabola into two equal parts.
- The vertex is the highest or lowest point of the parabola, indicating the maximum or minimum value depending on its orientation.
Standard Forms and Types
- Standard form of a quadratic function is given by f(x) = ax² + bx + c.
- Binomials are quadratic expressions featuring two terms.
- Trinomials consist of three terms, representing more complex quadratic expressions.
Solutions and Values
- A zero of a function occurs at point x where f(x) = 0, indicating the x-intercepts of the graph.
- The roots of an equation are values that satisfy the equation.
Transformation Techniques
- Completing the square involves adding a term to create a perfect square trinomial, facilitating easier graphing and analysis.
Imaginary and Complex Numbers
- The imaginary unit i equals √(-1), a fundamental concept in complex numbers.
- Imaginary numbers are defined as the square roots of negative numbers.
- A complex number is expressed in the form a + bi, where a is the real part and b is the imaginary part.
The Complex Plane
- Real part refers to complex numbers where b = 0, while the imaginary part consists of numbers where a = 0 and b ≠ 0.
- The complex conjugate of a + bi is a - bi, an important relationship in complex number operations.
- The complex plane represents real numbers on the horizontal axis and imaginary numbers on the vertical axis.
Quadratic Inequalities and Applications
- A quadratic inequality in two variables features real numbers a, b, and c, with a ≠ 0.
- The discriminant within the Quadratic Formula helps ascertain the number of real roots for a quadratic equation.
- Quadratic regression is a technique for generating a quadratic model based on a data set, useful in statistical analysis.
- A quadratic model is essentially a quadratic function that accurately reflects a given data set.
Studying That Suits You
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Description
Test your understanding of key concepts in Algebra 2 Chapter 5 with these flashcards. Covering essential terms such as quadratic functions, parabolas, and the axis of symmetry, this quiz will help reinforce your knowledge. Perfect for reviewing before exams or enhancing your understanding of algebra.