Question

Please help me ASAP

Answer 1

Answer:

The Graph is shown below

Step-by-step explanation:

The Graph of a Function

Given the function:

$\displaystyle y=g(x)=-\frac{3}{2}(x-2)^2$

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:

$\displaystyle y=g(-2)=-\frac{3}{2}(-2-2)^2=-\frac{3}{2}(-4)^2==-\frac{3}{2}*16=-24$

Point (-2,-24)

$\displaystyle y=g(0)=-\frac{3}{2}(0-2)^2=-\frac{3}{2}(-2)^2=-\frac{3}{2}*4=-6$

Point (0,-6)

$\displaystyle y=g(2)=-\frac{3}{2}(2-2)^2=-\frac{3}{2}(0)^2=0$

Point (2,0)

$\displaystyle y=g(4)=-\frac{3}{2}(4-2)^2=-\frac{3}{2}(2)^2=-\frac{3}{2}*4=-6$

Point (4,-6)

$\displaystyle y=g(6)=-\frac{3}{2}(6-2)^2=-\frac{3}{2}(4)^2=-\frac{3}{2}*16=-24$

Point (6,-24)

The graph is shown in the image below