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 5.1.12EP
The given function has a minimum value.
The minimum 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
Explanation :
For the function
Since the coefficient of ‘a’ is positive, the curve of this function is upward facingand hence the function has a minimum 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 minimum.
Thus, the minimum value 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 lesser than or equal to the minimum. That is,
Chapter EP Solutions
Algebra 2
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