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Concept explainers
a.
To decipher whether the function has a maximum or minimum value.
a.
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Answer to Problem 45PPS
The given function has a minimum value.
Explanation of Solution
Given information :
The function provided is
For the function
Since the coefficient of ‘a’ is positive, the curve of this function is upward facing and hence the function has a minimum value.
b.
To determine the maximum or minimum value of the given function.
b.
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Answer to Problem 45PPS
The function is minimum at - 48 .
Explanation of Solution
Given information :
The function provided is
Formula used :
Formula to compute the x-coordinate of the vertex is
Calculation :
Since the coefficient of ‘a’ is positive, the curve of this function is upward facing and hence the function has a minimum value.
X-coordinate of the vertex is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y , that will be the maximum.
Putting the value of
Simplifying the expression.
Thus, the minimum is at - 48 .
c.
To calculate the domain and range for the given function.
c.
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Answer to Problem 45PPS
The domain is all real numbers, that is,
Explanation of Solution
Given information :
The function provided is
Formula used :
Formula to compute the x-coordinate of the vertex is
Calculation :
Since the coefficient of ‘a’ is negative, the curve of this function is downward facing and hence the function has a maximum value.
X-coordinate of the vertex is
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
Simplifying
Vertex can be found out by putting the value of x computed in the axis of symmetry in the original function. This will give a value of y , that will be the maximum.
Putting the value of
Simplifying the expression.
Thus, the minimum is at - 48 .
Since x can take up any real values, the range is
Since the domain is the values of y, it can only take up values lesser than or equal to the maximum. That is,
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Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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