Concept explainers
a.
To decide whether the function has a maximum or minimum value.
a.
Answer to Problem 49PPS
The given function has a maximum value.
Explanation of Solution
Given information :
The function provided is
For the function
Since the coefficient of ‘a’ is negative, the curve of this function is downward facing and hence the function has a maximum value.
b.
To find the maximum or minimum value of the given function.
b.
Answer to Problem 49PPS
The maximum value is 3.
Explanation of Solution
Given information :
The function provided is
Formula used :
Formula to compute the x-coordinate of the vertex is
‘a’ and ‘b’ are coefficients
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
Here,
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
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 minimum.
Thus, the maximum value is 3.
c.
To calculate the domain and range for the given function.
c.
Answer to Problem 49PPS
The domain is all real numbers, that is,
Explanation of Solution
Given information :
The function provided 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
Here,
Formula for axis of symmetry.
Putting the values of ‘a’ and ‘b’ .
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 minimum.
Thus, the minimum value is 3.
Since x can take up any real values, the domain is
Since the range is the values of y, it can only take up values greater than or equal to the maximum. That is,
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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