A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from where it was thrown. A graphing calculator displays a quadratic function that models the ball's height, y, in feet, in terms of its horizontal distance, x, in feet. Answer parts (a)-(c) below. x, Ball's Horizontal Distance (feet) y, Ball's Height (feet) QuadReg y = ax? + bx + c a = - 0.9 6 1 8.1 3 6 b= 2.6 2.9 c = 6.1 a. Explain why a quadratic function was used to model the data. O A. The height increases then decreases, which looks like a quadratic function. O B. The height decreases quickly at first, but then decreases more slowly, which looks like a quadratic function. OC. The height decreases then increases, which looks like a quadratic function. O D. The height starts decreasing more and more rapidly, which looks like a quadratic function. In the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative? O A. Since the height of the ball starts at the height of the person throwing the ball, the quadratic graph must be shifted up, which makes a negative. O B. Since the height increases then decreases, the quadratic graph must open downward, not upward, which means a must be negative. OC. Since the height increases then decreases, the quadratic graph must open upward, not downward, which means a must be negative. b. Use the graphing calculator screen (shown in the box above) to express the model in function notation. f(x) =O c. Use the model from part (b) to determine the x-coordinate of the quadratic function's vertex. The x-coordinate of the vertex is. (Type an integer or a decimal rounded to one decimal place as needed.) Complete the statement below. The maximum height of the ball occurs feet from where it was thrown and the maximum height is feet. (Type integers or decimals rounded to one decimal place as needed.)
A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from where it was thrown. A graphing calculator displays a quadratic function that models the ball's height, y, in feet, in terms of its horizontal distance, x, in feet. Answer parts (a)-(c) below. x, Ball's Horizontal Distance (feet) y, Ball's Height (feet) QuadReg y = ax? + bx + c a = - 0.9 6 1 8.1 3 6 b= 2.6 2.9 c = 6.1 a. Explain why a quadratic function was used to model the data. O A. The height increases then decreases, which looks like a quadratic function. O B. The height decreases quickly at first, but then decreases more slowly, which looks like a quadratic function. OC. The height decreases then increases, which looks like a quadratic function. O D. The height starts decreasing more and more rapidly, which looks like a quadratic function. In the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative? O A. Since the height of the ball starts at the height of the person throwing the ball, the quadratic graph must be shifted up, which makes a negative. O B. Since the height increases then decreases, the quadratic graph must open downward, not upward, which means a must be negative. OC. Since the height increases then decreases, the quadratic graph must open upward, not downward, which means a must be negative. b. Use the graphing calculator screen (shown in the box above) to express the model in function notation. f(x) =O c. Use the model from part (b) to determine the x-coordinate of the quadratic function's vertex. The x-coordinate of the vertex is. (Type an integer or a decimal rounded to one decimal place as needed.) Complete the statement below. The maximum height of the ball occurs feet from where it was thrown and the maximum height is feet. (Type integers or decimals rounded to one decimal place as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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Question
Transcribed Image Text:A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from
where it was thrown. A graphing calculator displays a quadratic function that models the ball's height, y, in feet, in terms of its horizontal distance, x, in feet. Answer
parts (a)-(c) below.
x, Ball's Horizontal Distance (feet)
y, Ball's Height (feet)
QuadReg
y = ax? + bx + c
1
8.1
a = - 0.9
3
6
b= 2.6
c = 6.1
4
2.9
a. Explain why a quadratic function was used to model the data.
O A. The height increases then decreases, which looks like a quadratic function.
O B. The height decreases quickly at first, but then decreases more slowly, which looks like a quadratic function.
O C. The height decreases then increases, which looks like a quadratic function.
O D. The height starts decreasing more and more rapidly, which looks like a quadratic function.
In the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative?
O A. Since the height of the ball starts at the height of the person throwing the ball, the quadratic graph must be shifted up, which makes a negative.
O B. Since the height increases then decreases, the quadratic graph must open downward, not upward, which means a must be negative.
O C. Since the height increases then decreases, the quadratic graph must open upward, not downward, which means a must be negative.
b. Use the graphing calculator screen (shown in the box above) to express the model in function notation.
f(x) =O
c. Use the model from part (b) to determine the x-coordinate of the quadratic function's vertex.
The x-coordinate of the vertex is.
(Type an integer or a decimal rounded to one decimal place as needed.)
Complete the statement below.
The maximum height of the ball occurs
feet from where it was thrown and the maximum height is
feet.
(Type integers or decimals rounded to one decimal place as needed.)
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