Questions and Answers
Which graph represents the function f(x) = -x^2 + 5?
What is the range of the function f(x) = −(x + 5)(x + 1)?
What are the domain and range of the function f(x) = -x^2 - 2x + 15?
The domain is all real numbers. The range is {y | y ≤ 16}.
Which is one of the transformations applied to the graph of f(x) = x^2 to change it into the graph of g(x) = -x^2 + 16x - 44?
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Which translation maps the graph of the function f(x) = x^2 onto the function g(x) = x^2 + 2x + 6?
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What are the coordinates of the vertex of the graph for f(x) = x^2 + 4x − 5?
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What is the function written in vertex form for f(x) = 40x + 5x^2?
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What are the x-intercepts of the function f(x) = -2x^2 - 3x + 20?
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Which function does the graph represent if it is given?
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Which equation has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, -16)?
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What is true about the domain and range of the function f(x) = -(x + 3)(x - 1)?
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What are the missing values in the table for the projectile motion of a disc?
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What is the axis of symmetry for the function f(x)=7−4x+x^2?
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What is the function written in vertex form for f(x) = 4x^2 + 48x + 10?
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What is the function that represents the profit model given selling units?
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Study Notes
Function Representations
- The function f(x) = -x² + 5 is represented by a downward-opening parabola intersecting the y-axis at 5.
- For f(x) = −(x + 5)(x + 1), the range includes all real numbers less than or equal to 4.
Domain and Range
- The domain of f(x) = -x² - 2x + 15 is all real numbers. The range is {y | y ≤ 16}.
- The vertex for the function f(x) = x² + 4x - 5 is located at (-2, -9).
Graph Transformations
- The graph of f(x)=x² transformed into g(x) = -x² + 16x - 44 involves widening the original parabola.
- Translation of f(x) = x² to g(x) = x² + 2x + 6 shifts left 1 unit and up 5 units.
Symmetry and Intercepts
- The axis of symmetry for f(x) = x² + 4x - 5 is x = -2, indicating the vertex occurs at the point (-2, -9).
- The x-intercepts of f(x) = -2x² - 3x + 20 are at (-4, 0) and (0, -4).
Vertex Form Conversion
- The vertex form of f(x) = 40x + 5x² is derived as f(x) = 5(x + 4)² - 80.
- The conversion from f(x) = 4x² + 48x + 10 into vertex form yields f(x) = 4(x + 6)² - 26.
Profit Model
- A company's profit function modeled as f(x) = −2(x - 105)² + 18,050 indicates zero profit at 10 units sold and maximum profit at 105 units.
Relation to Projectile Motion
- In projectile motion, the disc's height values can be determined from the given intervals, resulting in A = 4 and B = 3 after computations.
Additional Properties
- The domain of f(x) = -(x + 3)(x - 1) is all real numbers, while its range includes values less than or equal to 4.
- The equation f(x) = -2(x - 2)(x - 4) models a graph with x-intercepts at (2, 0) and (4, 0), with a y-intercept at (0, -16).
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Description
This quiz tests your understanding of functions and their graphs in the context of Common Core Algebra I. You'll answer questions about specific quadratic equations and their characteristics. Prepare to apply your knowledge of algebra concepts!
