Questions and Answers
What is the standard form of a quadratic function?
What is a parabola?
A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.
What is the vertex form of a quadratic function?
f(x) = a(x - h)^2 + k
What is the slope-intercept form of a linear equation?
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What defines a quadratic equation?
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What is a root of an equation?
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What is a zero of an equation?
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What is a square root of a number?
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What is a complex number?
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What defines an imaginary number?
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What is 'completing the square'?
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What is the quadratic formula?
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What is the discriminant in a quadratic equation?
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Study Notes
Standard Form of a Quadratic Function
- A quadratic function is expressed as f(x) = ax² + bx + c, where a, b, c are real numbers and a ≠ 0.
- The graph of a quadratic function is called a parabola.
Parabola
- A parabola is a symmetrical open plane curve formed by the intersection of a cone and a plane parallel to its side.
- The trajectory of a projectile under gravity ideally follows a parabolic path.
Vertex Form
- The vertex form of a quadratic function is f(x) = a(x - h)² + k, with (h, k) representing the vertex of the parabola.
- Different textbooks may interpret "standard form" of a quadratic function variably.
Intercept Form
- Slope-intercept form is y = mx + b, where m represents the slope and b is the y-intercept.
Quadratic Equation
- A quadratic equation is defined as an equation of degree 2, with the highest exponent being 2.
- The standard form is expressed as y = ax² + bx + c, where a cannot be zero.
Root of an Equation
- A real number x is considered a root if it satisfies the equation.
- Roots correspond to the x-intercepts of the quadratic function, indicating intersection points with the x-axis.
Zero of an Equation
- A zero of a function is an input value that results in an output of zero.
- Zeros are identified as the x-coordinates where the graph intersects the x-axis, also known as x-intercepts.
Square Root
- A square root of a number a is a number y such that y² = a.
- For instance, both 4 and -4 are square roots of 16 since (4)² = (−4)² = 16.
Complex Numbers
- A complex number is expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit satisfying i² = -1.
- In a complex number, a represents the real part, while b denotes the imaginary part.
Imaginary Numbers
- Imaginary numbers can be represented as a real number multiplied by the imaginary unit i, defined by i² = -1.
- For example, 5i is an imaginary number, and its square results in -25.
Completing the Square
- Completing the square is a method for solving quadratic equations, graphing quadratic functions, and evaluating integrals.
- It is particularly useful when factoring does not yield sufficient results or to find irrational and complex roots.
Quadratic Formula
- The quadratic formula is utilized to solve quadratic equations and is represented as x = (-b ± √D) / (2a).
- A quadratic equation typically has two solutions, which are referred to as roots.
Discriminant
- The discriminant D = b² - 4ac is calculated from the coefficients of the equation ax² + bx + c = 0.
- The discriminant indicates the nature and type of roots the quadratic equation possesses.
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Description
Test your knowledge of key terms in Algebra 2 with these flashcards. This quiz covers important concepts such as the standard form of a quadratic function and the definition of a parabola. Perfect for students looking to reinforce their understanding of algebra vocabulary.
