a.
To Find: The quadratic model for the data.
The quadratic model for the data is
Given:
A man throws a ball off the top of a building and records the height of the ball at different times, as shown in the table.
Time | Height |
Explanation:
Given the points are:
Find the quadratic function using the standard form of
Substitute
Substitute
Substitute
Substitute
Eliminate the equation between
To get the value of
Multiply
Solve the equations
Substitute the value of
To find the value of
Now, substitute
Here
b.
To Estimate: The height of the ball at
The estimated height of the ball at
Given:
A man throws a ball off the top of a building and records the height of the ball at different times, as shown in the table.
Time | Height |
Explanation:
Estimate the height of the ball at
From part
Substitute
Thus, the estimated height of the ball at
c.
To Determine: The maximum height of the ball.
The maximum height of the ball is
Given:
A man throws a ball off the top of a building and records the height of the ball at different times, as shown in the table.
Time | Height |
Explanation:
Find the maximum height of the ball,
From part
The maximum value of the function denoted by maximum height the ball.
For any quadratic function, the maximum value
Here
From the equation
Substitute the above data into the formula
Thus, the maximum height of the ball is
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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