1 1/2 as a fraction
1 answer:
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The <em>correct answers</em> are:
C) No: we would need to know if the vertex is a minimum or a maximum; and
C)( 0.25, 5.875).
Explanation:
The domain of any quadratic function is all real numbers.
The range, however, would depend on whether the quadratic was open upward or downward. If the vertex is a maximum, then the quadratic opens down and the range is all values of y less than or equal to the y-coordinate of the vertex.
If the vertex is a minimum, then the quadratic opens up and the range is all values of y greater than or equal to the y-coordinate of the vertex.
There is no way to identify from the coordinates of the vertex whether it is a maximum or a minimum, so we cannot tell what the range is.
The graph of the quadratic function is shown in the attachment. Tracing it, the vertex is at approximately (0.25, 0.5875).
Part A
Given that
Then,
For
, then
Thus,
For
, we have
Part B
Recall that from part A,
Now, at initial position, t = 0 and
, thus we have
and when the velocity drops to half its value,
and 
Thus,
Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by
Given that
Then,
For
Thus,
For
Part B
Recall that from part A,
Now, at initial position, t = 0 and
and when the velocity drops to half its value,
Thus,
Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by