Questions and Answers
What is a quadratic function?
A function in which the greatest power of the variable is 2.
What is the vertex of a parabola?
The maximum or minimum point of a parabola.
What is the axis of symmetry?
A line that divides a plane figure or a graph into two congruent reflected halves.
What does maximum refer to in a parabola?
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What does minimum refer to in a parabola?
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What is the domain in a quadratic function?
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What is the range in a quadratic function?
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What is a solution in the context of a graph?
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What is the standard form of a quadratic function?
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What does the equation y = x^2 + k do?
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What does the equation y = (x + h)^2 do?
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What does the equation y = ax^2 when a is a fraction do?
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What does the equation y = ax^2 when a is a whole number do?
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What happens to the graph when a in y = ax^2 is negative?
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What is completing the square?
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What is the Quadratic Formula?
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What are first differences in a table?
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What are second differences in a table?
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What is a step function?
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What is an absolute value function?
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What is an exponential function?
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What is a linear function?
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Study Notes
Quadratic Functions and Characteristics
- Quadratic function: A mathematical function characterized by the variable raised to the greatest power of 2.
- Vertex: The turning point of a parabola, representing either its maximum or minimum value.
- Axis of Symmetry: A vertical line that divides a parabola into two mirror-image halves.
Maximum and Minimum Values
- Maximum: The highest point on a downward-opening parabola, occurring when the coefficient of x squared is negative.
- Minimum: The lowest point on an upward-opening parabola, occurring when the coefficient of x squared is positive.
Domain and Range
- Domain: All possible values for the variable x in a function.
- Range: All possible values for the variable y generated by a function.
Solutions and Forms of Quadratic Functions
- Solution: The x-coordinate(s) where the graph intersects the x-axis.
- Standard form of quadratic function: Typically represented as y = ax^2 + bx + c, where a, b, and c are constants.
Transformations of Quadratic Functions
- y = x^2 + k: Translates the graph vertically by k units.
- y = (x+h)^2: Translates the graph horizontally by h units.
- y = ax^2 when a is a fraction: Makes the graph wider due to the smaller value of a.
- y = ax^2 when a is a whole number: Makes the graph narrower as a increases.
- y = ax^2 when a is negative: Inverts the graph, flipping it upside down.
Special Techniques and Related Functions
- Completing the square: A method used to transform a quadratic expression into a perfect square trinomial of the form (x+b)^2 = x^2 + 2bx + b^2.
- Quadratic Formula: A tool used for finding roots of quadratic equations; however, no specific definition provided.
Differences in Functions
- First Differences: If the differences of consecutive outputs in a table are consistent, the relationship is linear.
- Second Differences: If the differences of consecutive first differences are consistent, the relationship is quadratic.
Additional Function Types
- Step function: Exhibits discrete jumps and is represented graphically by a series of connected line segments.
- Absolute Value Function: Expressed as y = |x|, produces a V-shaped graph.
- Exponential function: Defined as y = ab^x, where a is a constant and b is the base.
- Linear function: A function that generates a straight line graph.
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Description
Explore the key concepts of quadratic functions through this quiz. Understand the properties of parabolas, including their vertex, axis of symmetry, and the calculation of maximum and minimum values. Test your knowledge on the domain, range, and standard form of quadratic functions.
