4. Polynomial Functions

Quadratic Functions

Textbook Question
In Exercises 17–38, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=2x−x²−2
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Textbook Question
In Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=3x^2−12x−1
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Textbook Question
In Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=−4x^2+8x−3
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Textbook Question
In Exercises 39–44, an equation of a quadratic function is given. a) Determine, without graphing, whether the function has a minimum value or a maximum value. b) Find the minimum or maximum value and determine where it occurs. c) Identify the function's domain and its range. f(x)=5x²−5x
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Textbook Question
In Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. The vertex is and the parabola opens up.
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Textbook Question
Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; b^2 - 4ac = 0
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Textbook Question
In Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. Maximum = -6 at x = 10
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Textbook Question
Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) a < 0; ^b2 - 4ac < 0
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Textbook Question
In Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x^2 but with the given point as the vertex. (5, 3)
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Textbook Question
Several graphs of the quadratic function ƒ(x) = ax^2 + bx + c are shown below. For the given restrictions on a, b, and c, select the corresponding graph from choices A–F. (Hint: Use the discriminant.) A > 0; b^2 - 4ac > 0
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Textbook Question
In Exercises 49–52, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x² but with the given point as the vertex. (−10, −5)
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Textbook Question
Connecting Graphs with Equations Find a quadratic function f having the graphshown. (Hint: See the Note following Example 3.)
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Textbook Question
In Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x² or g(x) = -3x², but with the given maximum or minimum. Maximum = 4 at x = -2
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Textbook Question
Connecting Graphs with Equations Find a quadratic function f having the graphshown. (Hint: See the Note following Example 3.)
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Textbook Question
In Exercises 53–56, write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x² or g(x) = -3x², but with the given maximum or minimum. Minimum = 0 at x = 11
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