Questions and Answers
What is the formula to find the vertex of a quadratic function?
x = -b/2a
What is a rational number?
a number that can be expressed as the quotient or fraction of two integers
What is ALWAYS the domain for a quadratic function?
(-∞, ∞)
What is the standard form of a quadratic function?
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What is ALWAYS the Y-intercept in a linear function (mx+b)?
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What is a function?
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What is a vertex?
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What is the vertex of the equation y = 3(x - 3)^2 + 5?
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What is slope in terms of a function?
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What is the slope of the equation y = 2x + 3?
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If x > 3, then what part of the graph is shaded?
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What is the zero(s) of a function?
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Study Notes
Quadratic Functions and Their Properties
- The vertex of a quadratic function can be found using the formula: x = -b/2a.
- The domain of any quadratic function is always (-∞, ∞), meaning it includes all real numbers.
- The standard form of a quadratic function is represented as f(x) = ax² + bx + c.
- A vertex is defined as the intersection of the parabola with its axis of symmetry, indicating the maximum or minimum point on the graph.
Functions and Their Characteristics
- A rational number can be expressed as the quotient of two integers, such as a/b where b ≠ 0.
- A function is defined as a relationship where each input is associated with one output.
- In a linear function represented as mx + b, the b value signifies the Y-intercept, or initial value of the function.
Slope and Its Interpretation
- The slope of a function indicates how much the output (y value) changes for a unit change in the input (x value), represented by the coefficient m in mx + b.
- For the linear function y = 2x + 3, the slope is exactly 2.
Graphical Analysis
- If x > 3, the shaded portion of the graph corresponds to the region from 3 to infinity, illustrating where the inequality holds true.
- The zero(s) of a function are the x-values where the output (y) equals zero.
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Test your knowledge with these Algebra 1 flashcards. Each card covers key concepts such as quadratic functions, rational numbers, and their properties. Perfect for quick reviews and mastering the essentials of Algebra 1.