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Questions and Answers
Refer to the graph shown. Write down the coordinates of the vertex.
Refer to the graph shown. Write down the coordinates of the vertex.
(4, 1)
Refer to the graph shown. Write the equation in the form y = 3(x − h)² + k
Refer to the graph shown. Write the equation in the form y = 3(x − h)² + k
y = 3(x - 4)² + 1
Refer to the graph shown. Write down the equation of the axis of symmetry.
Refer to the graph shown. Write down the equation of the axis of symmetry.
x = 4
Refer to the graph shown. Write down the domain and range.
Refer to the graph shown. Write down the domain and range.
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Write down the coordinates of the vertex.
Write down the coordinates of the vertex.
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Sketch the graph of the parent quadratic, y = _x_², and the graph of y = g(x) on the same axes. Then write down the coordinates of the vertex and the equation of the axis of symmetry for the graph of g. g(x) = (x + 3)²
Sketch the graph of the parent quadratic, y = _x_², and the graph of y = g(x) on the same axes. Then write down the coordinates of the vertex and the equation of the axis of symmetry for the graph of g. g(x) = (x + 3)²
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Sketch the graph of the parent quadratic, y = _x_², and the graph of y = g(x) on the same axes. Then write down the coordinates of the vertex and the equation of the axis of symmetry for the graph of g. g(x) = −_x_² + 4
Sketch the graph of the parent quadratic, y = _x_², and the graph of y = g(x) on the same axes. Then write down the coordinates of the vertex and the equation of the axis of symmetry for the graph of g. g(x) = −_x_² + 4
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Sketch the graph of the parent quadratic, y = _x_², and the graph of y = g(x) on the same axes. Then write down the coordinates of the vertex and the equation of the axis of symmetry for the graph of g. g(x) = 2(x − 4)² − 3
Sketch the graph of the parent quadratic, y = _x_², and the graph of y = g(x) on the same axes. Then write down the coordinates of the vertex and the equation of the axis of symmetry for the graph of g. g(x) = 2(x − 4)² − 3
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Describe the transformations of the graph of f(x) = _x_² that lead to the graph of g. Then write an equation for g(x).
Describe the transformations of the graph of f(x) = _x_² that lead to the graph of g. Then write an equation for g(x).
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What are the x-intercepts of the quadratic function f(x) = (x - 3)^2 - 2?
What are the x-intercepts of the quadratic function f(x) = (x - 3)^2 - 2?
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Find the coordinates of the vertex of the quadratic function f(x) = -2x^2 + 4x - 8?
Find the coordinates of the vertex of the quadratic function f(x) = -2x^2 + 4x - 8?
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Match the following transformations with the corresponding effect on the graph of the quadratic function f(x) = x^2:
Match the following transformations with the corresponding effect on the graph of the quadratic function f(x) = x^2:
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Find the equation of the axis of symmetry for the function f(x) = 3x^2 + 18x + 20?
Find the equation of the axis of symmetry for the function f(x) = 3x^2 + 18x + 20?
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What are the x-intercepts of the quadratic function f(x) = x^2-12x+36?
What are the x-intercepts of the quadratic function f(x) = x^2-12x+36?
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Find the coordinates of the point of intersection between the graphs of the functions f(x) = x^2 - 8x + 5 and g(x) = 3x^2 - 6x + 2?
Find the coordinates of the point of intersection between the graphs of the functions f(x) = x^2 - 8x + 5 and g(x) = 3x^2 - 6x + 2?
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The graphs of the functions f(x) = x^2 - 8x + 5 and g(x) = -2x^2 - 8x - 11 intersect at two points.
The graphs of the functions f(x) = x^2 - 8x + 5 and g(x) = -2x^2 - 8x - 11 intersect at two points.
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What is the equation of the axis of symmetry for the quadratic function f(x) = 2(x + 3)(x - 1)?
What is the equation of the axis of symmetry for the quadratic function f(x) = 2(x + 3)(x - 1)?
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Find the coordinates of the vertex of the quadratic function f(x) = -3(x - 2)^2 + 5?
Find the coordinates of the vertex of the quadratic function f(x) = -3(x - 2)^2 + 5?
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What are the x-intercepts of the quadratic function f(x) = 2x^2 + 6x + 3?
What are the x-intercepts of the quadratic function f(x) = 2x^2 + 6x + 3?
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What is the equation of the axis of symmetry of the function f(x) = 4(x + 3)(x - 1)?
What is the equation of the axis of symmetry of the function f(x) = 4(x + 3)(x - 1)?
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Study Notes
Quadratic Functions and Transformations
- Various quadratic functions are presented, along with their corresponding graphs.
- Key features, such as vertex coordinates, intercepts, axis of symmetry, domain, and range, are identified for each function.
- Students need to label these key features on sketches of the functions.
Exercise 3J
- Problems involve sketching parent quadratic functions (y = x²) and related functions (g(x)) on the same axes.
- Coordinates of the vertex and the axis of symmetry need to be determined for each transformed quadratic.
Exercise 3L
- Students use a graphing calculator (GDC) to plot quadratic functions.
- Key features (x-intercepts, y-intercepts, vertex) need to be identified and labeled on the graph.
- Domain and range of the functions are required.
Exercise 3M
- Problems focus on determining the equation of symmetry, coordinates of the vertex, and y-intercept of various quadratic functions.
Exercise 3N
- Students are required to express quadratic functions in the form f(x) = a(x - p)(x - q), where p > q.
- Finding the x-intercepts and y-intercept coordinates of the function is also part of this exercise.
Exercise 3R
- Finding the exact values and graphical solutions for quadratic equations.
- Determining the points of intersection of specified quadratic and linear functions through graphical methods.
Exercise 3W
- Solving quadratic inequalities graphically.
- Identifying the values of constants that cause quadratic equations to have two distinct real roots or no real roots.
Exercise 3X
- The length of the base of a triangle is related to its height and area. A function models the ball's height over time.
Exercise 30
- Finding the expression for quadratic functions using given information from their graphs.
Exercise 3P
- Various problems involving quadratic functions and their transformations.
Exercise 3S
- A variety of problems related to quadratic functions require finding key features such as roots, vertex, and symmetry. A variety of quadratic problems.
Exam-Style Questions
- Problem types related to quadratic functions and their transformations appear throughout the exercises.
- Finding solutions and describing these types of transformations of the functions are frequent tasks.
Review
- Problems involve identifying features of graphs of quadratic functions and calculating important components like the vertex, axis of symmetry, and intercepts, as well as describing transformations.
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Description
Test your knowledge on quadratic functions and their transformations. This quiz covers key features like vertex coordinates, intercepts, domain, and range. You'll sketch graphs, identify characteristics, and utilize graphing calculators to deepen your understanding of these essential concepts.
