Find the fourth degree polynomial function with zeros 6,-6,6i
2 answers:
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Given:
The function is:
To find:
Express the quadratic equation in the form of , then state the minimum or maximum value,axis of symmetry and minimum or maximum point.
Solution:
The vertex form of a quadratic function is:
...(i)
Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.
We have,
It can be written as:
Adding and subtracting square of half of coefficient of x inside the parenthesis, we get
...(ii)
On comparing (i) and (ii), we get
Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.
Maximum value = 10.125
Axis of symmetry :
Maximum point = (1.75,10.125)
Therefore, the vertex form of the given function is , the maximum value is 10.125, the axis of symmetry is
and the maximum point is (1.75,10.125).