Answer:
<em>The Graph is shown below</em>
Step-by-step explanation:
<u>The Graph of a Function</u>
Given the function:
![\displaystyle y=g(x)=-\frac{3}{2}(x-2)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%28x%29%3D-%5Cfrac%7B3%7D%7B2%7D%28x-2%29%5E2)
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](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%28-2%29%3D-%5Cfrac%7B3%7D%7B2%7D%28-2-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%28-4%29%5E2%3D%3D-%5Cfrac%7B3%7D%7B2%7D%2A16%3D-24)
Point (-2,-24)
![\displaystyle y=g(0)=-\frac{3}{2}(0-2)^2=-\frac{3}{2}(-2)^2=-\frac{3}{2}*4=-6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%280%29%3D-%5Cfrac%7B3%7D%7B2%7D%280-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%28-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%2A4%3D-6)
Point (0,-6)
![\displaystyle y=g(2)=-\frac{3}{2}(2-2)^2=-\frac{3}{2}(0)^2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%282%29%3D-%5Cfrac%7B3%7D%7B2%7D%282-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%280%29%5E2%3D0)
Point (2,0)
![\displaystyle y=g(4)=-\frac{3}{2}(4-2)^2=-\frac{3}{2}(2)^2=-\frac{3}{2}*4=-6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%284%29%3D-%5Cfrac%7B3%7D%7B2%7D%284-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%282%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%2A4%3D-6)
Point (4,-6)
![\displaystyle y=g(6)=-\frac{3}{2}(6-2)^2=-\frac{3}{2}(4)^2=-\frac{3}{2}*16=-24](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3Dg%286%29%3D-%5Cfrac%7B3%7D%7B2%7D%286-2%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%284%29%5E2%3D-%5Cfrac%7B3%7D%7B2%7D%2A16%3D-24)
Point (6,-24)
The graph is shown in the image below
Answer:
and ![y=-1](https://tex.z-dn.net/?f=y%3D-1)
Step-by-step explanation:
If two equations are given, we can solve one of the equation in terms of single variable and put it in the other equation which will further give the value of x and y.
For the given equations:
Equation:1
Equation:2
Solving equation multiply equation 2 with 4 on both the sides
Equation 3
Subtracting Equation:3 from Equation:1
![8x-5y-(8x+36y)=21-(-20)\\8x-5y-8x-36y=21+20\\-41y=41\\y=-1](https://tex.z-dn.net/?f=8x-5y-%288x%2B36y%29%3D21-%28-20%29%5C%5C8x-5y-8x-36y%3D21%2B20%5C%5C-41y%3D41%5C%5Cy%3D-1)
Putting value of 'y' in Equation:2 which will give the value of x
![2x+9y=-5\\2x+9(-1)=-5\\2x-9=-5\\2x=4\\x=2](https://tex.z-dn.net/?f=2x%2B9y%3D-5%5C%5C2x%2B9%28-1%29%3D-5%5C%5C2x-9%3D-5%5C%5C2x%3D4%5C%5Cx%3D2)
This is the the concept of trigonometry, to get the sine value of the the function given we shall proceed as follows;
Using Pythagorean theorem, the hypotenuse of the triangle will be found as follows;
The side length will be 8 units since the y-coordinate is -8
The side width will be 3 units since the x- coordinate is 3
c^2=a^2+b^2
c^2=(3)^2+(-8)^2
c^2=9+64
c^2=73
c=sqrt(73)
Therefore the sine value will be:
sin x=3/sqrt(73)
multiply both numerator and denominator by sqrt(73) we get:
sin x=(3√73)/73
Therefore the answer is A]