The table shows the length and area of a square patio whose equation is y=12x−x^{2} where x represents the length of the side of the patio and y represents the area of the patio.

What does the point (6, 36) represent graphically?

A) the y-intercept

B)the vertex

C) the minimum point

D) the x-intercept

x y

1 11

2 20

3 27

4 32

5 35

6 36

7 35

jjennylove Jan 8, 2019

#1**+1 **

It represents the vertex.....we can see this as follows

y = -x^2 + 12x the x coordinatee of the vertex is given by :

-12 / [ 2 * -1 ] = -12 / -2 = 6

To find the y coordinate of the vertex, put 6 back into the function

y = -(6)^2 + 12(6) = -36 + 72 = 36

So....the vertex is (x, y) = ( 6, 36)

CPhill Jan 8, 2019