Questions and Answers
The graph of a quadratic function is non-linear; it is a _____ (U-Shape).
Parabola
The equation of a quadratic function is a ____ polynomial; it includes an ax² term.
quadratic
What is the standard form of a quadratic function?
ax² + bx + c
In standard form, c = the _______.
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The vertical fold line that makes the halves of the parabola match is called the ____________.
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In standard form, if a > 0 then the vertex is the (minimum/maximum).
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In standard form, if a < 0 then the vertex is the (minimum/maximum).
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Domain is all the ______ values, range is all the _______ values.
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The formula for the line of the axis of symmetry is x=___. It is also the x-value of the vertex.
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A parabola must have __ points plotted.
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The x-intercepts of a function are called ___.
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What is the PARENT function of a quadratic equation?
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The opposite of ( )² is ___; they undo each other.
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The quadratic formula is x = _______.
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If you only need to see the key features of a parabola and you have time, you can use the _____ method to find the zeros.
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If the function is factorable, use the _____ method to find the zeros.
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If the function has no 'bx' term, use the _____ method to find the zeros.
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If the function is not factorable and has a 'bx' term, use the ______ method to find the zeros.
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Study Notes
Quadratic Functions Overview
- A quadratic function's graph takes the shape of a parabola, characterized by a U-shape.
- The equation of a quadratic function is a quadratic polynomial, specifically containing an ax² term.
Standard Form of Quadratic Equation
- The standard form of a quadratic function is represented as y = ax² + bx + c.
- In this form, the y-intercept is given by the constant term c.
Key Features of Parabolas
- The axis of symmetry is a vertical fold line where both halves of the parabola are mirror images.
- When a > 0, the vertex represents a minimum, indicating the parabola opens upward.
- Conversely, if a < 0, the vertex is a maximum, with the parabola opening downward.
Domain and Range
- The domain refers to all possible x values, while the range includes all possible y values.
Finding Key Points and Zeros
- The formula for the axis of symmetry, which also gives the x-value of the vertex, is x = -b/2a.
- To effectively plot a parabola, it’s recommended to have 5 points plotted.
- The x-intercepts of a function are referred to as zeros, roots, or solutions.
Parent Function and Operations
- The parent function for quadratic equations is y = x².
- The operation that inverses squaring is the square root (√), as they undo each other.
Methods to Find Zeros
- To see the key features of a parabola, the graphing method can be employed to find zeros.
- If the quadratic function is factorable, the Zero Product Property should be used to find the zeros.
- When the function lacks a bx term, utilize the Square Root Property for finding zeros.
- If the quadratic is not factorable and includes a bx term, apply the Quadratic Formula:
- x = (-b ± √(b² − 4ac)) ÷ 2a*.
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Test your knowledge of quadratic functions with these flashcards. Each card presents important concepts, definitions, and standard forms related to quadratic functions in Algebra 1. Enhance your understanding and prepare for your exams effectively.
