A banner is hung for a party . The distance from a point on the bottom edge of the banner to the floor can be determined by using the function f(x)= 0.25x² -x+9.5, where x is the distance , in feet , of the point from the left end of the banner . How high above the floor is the lowest point on the bottom edge of the banner , Explain.

The correct answer is: 8.5

Solution:- We have given a function of banner hung.
f(x) = 0.25x² -x+9.5,
We have to find the height of lowest point of the banner
The lowest point will be the vertex of the curve, so the lowest height will be y- coordinate of the vertex
On comparing with the standard form of the function f(x)=ax²+bx+c.
In f(x)= 0.25x² -x+9.5,,  a= 0.25, b= -1, and c=9.5,  So, the equation for the axis of symmetry is given by

x = −(-1)/2(0.25)

x = 1/0.5

x = 2
The equation of the axis of symmetry for f(x)= 0.25x² -x+9.5,  is x = 2.
The x coordinate of the vertex is the same:

h = 2
The y coordinate of the vertex is :

k = f(h)

k = 0.25h² -h+9.5,

k = 0.25(2)² -2+9.5,

k = 1 - 2 + 9.5

k = 8.5
Therefore, the vertex is (2 , 8.5)
The lowest height will be the y-coordinate of vertex = 8.5