Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing.
(a) The vertex is
(Type an ordered pair, using integers or fractions.)
(b) Determine whether the parabola has a maximum value or a minimum value and find the value.
Select the correct choice below and fill in the answer box within your choice.
(Type an integer or a fraction.)
A. The parabola opens upward and has a minimum value of
B. The parabola opens downward and has a maximum value of
(c) What is the range of
The range of
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
(d) On what interval is the function increasing?
The function is increasing on
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
On what interval is the function decreasing?
The function is decreasing on
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
Answer
Step 1 ：The given function is a quadratic function in the form of
Step 2 ：The vertex of a parabola
Step 3 ：Since the coefficient of
Step 4 ：The range of the function is all the y-values that the function can take. Since the parabola opens upward and has a minimum value, the range is
Step 5 ：The function is increasing on the interval
Step 6 ：Calculating these values, we find that the vertex is
Step 7 ：The parabola opens upward and has a minimum value of
Step 8 ：The range of
Step 9 ：The function is increasing on the interval
Step 10 ：
Step 11 ：
Step 12 ：
Step 13 ：
Step 14 ：
