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# 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)= 0.25x^{2} -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) = 0.25x^{2} -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)=ax^{2}+bx+c.

In f(x)= 0.25x^{2} -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)= 0.25x^{2} -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 = 0.25h^{2} -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

The equation of the axis of symmetry for f(x)= 0.25x

^{2}-x+9.5, is x = 2.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}-h+9.5,

^{2}-2+9.5,

Therefore, the vertex is (2 , 8.5)

The lowest height will be the y-coordinate of vertex = 8.5

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