Answer:
The Graph is shown below
Step-by-step explanation:
The Graph of a Function
Given the function:
[tex]\displaystyle y=g(x)=-\frac{3}{2}(x-2)^2[/tex]
It's required to plot the graph of g(x). Let's give x some values:
x={-2,0,2,4,6}
And calculate the values of y:
[tex]\displaystyle y=g(-2)=-\frac{3}{2}(-2-2)^2=-\frac{3}{2}(-4)^2==-\frac{3}{2}*16=-24[/tex]
Point (-2,-24)
[tex]\displaystyle y=g(0)=-\frac{3}{2}(0-2)^2=-\frac{3}{2}(-2)^2=-\frac{3}{2}*4=-6[/tex]
Point (0,-6)
[tex]\displaystyle y=g(2)=-\frac{3}{2}(2-2)^2=-\frac{3}{2}(0)^2=0[/tex]
Point (2,0)
[tex]\displaystyle y=g(4)=-\frac{3}{2}(4-2)^2=-\frac{3}{2}(2)^2=-\frac{3}{2}*4=-6[/tex]
Point (4,-6)
[tex]\displaystyle y=g(6)=-\frac{3}{2}(6-2)^2=-\frac{3}{2}(4)^2=-\frac{3}{2}*16=-24[/tex]
Point (6,-24)
The graph is shown in the image below
