The path of a rock released from a catapult is modeled by 
. The coordinates x and y are measured in feet, with x = 0 corresponding to the position from which the ball was thrown. Find the highest point and range of the trajectory. Hint: The highest point is the y value of the vertex of the parabola, and the range is the positive x value where y = 0.
A. highest point: 10 ft range: 160 ft
B. highest point: 40 ft range: 160 ft
C. highest point: 10 ft range: 40 ft
D. highest point: 10 ft range: 40 + 
ft
E. highest point: 40 ft range: 80 ft
Answer: D
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Provide an appropriate response.The curves y = ax2 + b and y = 2x2 + cx have a common tangent line at the point (-1, 0). Find a, b, and c.
A. a - 2, b = 1, c = -1 B. a = 1, b = -1, c = 2 C. a = -1, b = 1, c = -2 D. a = 1, b = 0, c = 2
Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ? The least-squares line must pass through at least one data point. ?
A. It is false.
?
Example. Find the least-squares line for the data
?
?
Solution. Here, we have 
and
?
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 |  |  |  |  |
?
?
The least-squares line for the data is given by linear equation
?
?
where the constants m and b satisfy the normal equations
?
?
?
?
Then, we obtain the normal equations
?
?
Solving them, we found 
?
Therefore, the required least-squares line is 
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The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.
?
B. It is true
?
Suppose that we are given two data points
?
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If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amountsd1,d2, respectively.
?
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The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares
?
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be made as small as possible. But it is possible only in case when least-squares line passes through at least one data point.
The graph of the function y = f(x) is given below. Sketch the graph of y = 
.
A. 
B. 
C. 
D. 
Determine if the given sequence could be an arithmetic sequence.
, 
, 
, 
, 
, . . .
A. Yes B. No