To decide whether the function has a maximum or minimum value and to find the maximum or minimum value of the given function. Also to state the domain and range for the given function.
Answer to Problem 5.1.13EP
The given function has a maximumvalue.
The maximum value is
The domain is all real numbers, that is,
Explanation of Solution
Given information:
The function provided is
Formula used:
For the quadratic function
Formula to compute the x -coordinate of the vertex is
‘a’ and ‘b’ are coefficients
For the function
Since the coefficient of ‘a’ is negative, the curve of this function is downward facingand hence the function has a maximum value.
x -coordinate of the vertex is
Here,
Formula for axis of symmetry.
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.
Thus, the maximumvalue is
Since x can take up any real values, the domainis
Since the range is the values of y, it can only take up values greater than or equal to the maximum. That is,
Chapter EP Solutions
Algebra 2
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