Question

Please help me ASAP

Answer 1

The Graph is shown below

Explanation:

The Graph of a Function

Given the function:

`\displaystyle y=g(x)=-(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)=-(3)/(2)(-2-2)^2=-(3)/(2)(-4)^2==-(3)/(2)*16=-24`

Point (-2,-24)

`\displaystyle y=g(0)=-(3)/(2)(0-2)^2=-(3)/(2)(-2)^2=-(3)/(2)*4=-6`

Point (0,-6)

`\displaystyle y=g(2)=-(3)/(2)(2-2)^2=-(3)/(2)(0)^2=0`

Point (2,0)

`\displaystyle y=g(4)=-(3)/(2)(4-2)^2=-(3)/(2)(2)^2=-(3)/(2)*4=-6`

Point (4,-6)

`\displaystyle y=g(6)=-(3)/(2)(6-2)^2=-(3)/(2)(4)^2=-(3)/(2)*16=-24`

Point (6,-24)

The graph is shown in the image below