Chapter 3 Quiz: Quadratics
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If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high, the height of the ball can be modeled by the function where t is the number of seconds after the ball is thrown. What is the maximum height that the ball will reach?
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2 feet
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768 feet
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292 feet
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244 feet
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This Chapter 3 Quiz on Quadratics assesses understanding of quadratic functions and equations. It includes solving for vertex coordinates, factoring quadratic equations, and applying the quadratic formula, enhancing problem-solving skills in algebra.
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- 2.
Give the coordinates of the vertex for the quadratic function
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(-3, 4)
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(3, 4)
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(-3, -4)
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(3, -4)
Correct Answer
A. (3, 4)Explanation
The coordinates (3, 4) represent the vertex of the quadratic function. In a quadratic function in the form of y = ax^2 + bx + c, the vertex is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the value of y at the x-coordinate (-b/2a). In this case, since the x-coordinate is 3, the y-coordinate is given by f(3). Since the y-coordinate is 4, it means that f(3) = 4, which confirms that the vertex is indeed at (3, 4).Rate this question:
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- 3.
Solve for x using the square root method:
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7 and -1
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7
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-7 and 1
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259
Correct Answer
A. 7 and -1Explanation
The correct answer is 7 and -1. These are the values of x that satisfy the given equation when using the square root method.Rate this question:
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- 4.
Solve for x using factoring:
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-4 and -3/2
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8 and 3
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-8 and -3
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4 and 3/2
Correct Answer
A. 4 and 3/2Explanation
The correct answer is 4 and 3/2. To solve for x using factoring, we need to find the factors of the given numbers that add up to the coefficient of x. In this case, the coefficient of x is 1. The factors of 4 that add up to 1 are 4 and 1. The factors of 3/2 that add up to 1 are 3/2 and 1/2. Therefore, the solutions for x are 4 and 3/2.Rate this question:
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- 5.
Solve using the quadratic formula: Answer Choices: 1) 2) 3) 4)
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Option 1
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Option 2
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Option 3
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Option 4
Correct Answer
A. Option 2 -
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Solve for x using factoring:
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-5 and 2
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-10 and 1
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-2 and 5
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5 and 2
Correct Answer
A. -2 and 5Explanation
The correct answer is -2 and 5. To solve for x using factoring, we need to find two numbers that multiply to give the constant term (in this case, -10) and add up to give the coefficient of the linear term (in this case, 1). The numbers -2 and 5 satisfy these conditions because -2 * 5 = -10 and -2 + 5 = 1. Therefore, the solutions for x are -2 and 5.Rate this question:
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- 7.
Give the coordinates for the vertex of the quadratic function .
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(-1, 8)
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(1, 0)
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(-4, -10)
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(-1, 12)
Correct Answer
A. (-1, 8)Explanation
The vertex of a quadratic function is the point where the function reaches its maximum or minimum value. In this case, the vertex is given as (-1, 8). This means that the quadratic function reaches its maximum value at x = -1, and the corresponding y-value is 8.Rate this question:
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- 8.
Find the equation of the quadratic function whose graph is a parabola passing through the points (0, -3), (4, 37) and (-3, 30).
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Y = 16x^2 + 4x - 3
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Y = 3x^2 + 2x - 3
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Y = 3x^2 - 2x - 3
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Y = 4x - 3
Correct Answer
A. Y = 3x^2 - 2x - 3Explanation
The equation y = 3x^2 - 2x - 3 represents the quadratic function whose graph is a parabola passing through the points (0, -3), (4, 37), and (-3, 30). This equation is in the standard form of a quadratic function, y = ax^2 + bx + c, where a = 3, b = -2, and c = -3. By substituting the x and y values of the given points into the equation, we can verify that they satisfy the equation and lie on the graph of the parabola.Rate this question:
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- 9.
If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high, the height of the ball can be modeled by the function where t is the number of seconds after the ball is thrown. How long will it take the ball to hit the ground?
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6.905 seconds
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0.905 seconds
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-0.905 and 6.905 seconds
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7 seconds
Correct Answer
A. 6.905 seconds -
- 10.
Using the table on page 225 #28 in your textbook, find a quadratic model that fits the data in the table with x = 0 in 1900.
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Y = 0.003x^2 + 0.322x + 16.657
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Y = 0.003x^2 - 0.322x + 16.657
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Y = -0.024x + 11.474
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Y = -2.054x^2 + 36.216x - 73.881
Correct Answer
A. Y = 0.003x^2 - 0.322x + 16.657Explanation
The correct answer is y = 0.003x^2 - 0.322x + 16.657. This quadratic model fits the data in the table with x = 0 in 1900. The equation represents a quadratic function with a positive coefficient for the x^2 term (0.003), indicating an upward-opening parabola. The coefficient for the x term (-0.322) represents the slope of the quadratic function, and the constant term (16.657) represents the y-intercept. This equation accurately represents the relationship between x (years) and y (some variable) based on the given data.Rate this question:
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May 27, 2024Quiz Edited by
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Jun 24, 2013Quiz Created by
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