Write the quadratic function the points are (-1,35) (0,22) (1,11) (2,2) and (3,-5)

Step-by-step explanation:

We only need 3 of those points and the standard form of the quadratic to find the function.  The standard form is

From each coordinate we will sub in the x and y values.  I am going to use the following 3 points from the table. (0, 22), (1, 11) and (2, 2).  Always start with a coordinate that has an x value of 0 if you can!  Filling in the standard form with the first of those 3 coordinates:

simplifies down to the fact that c = 22. That's good to know; now we have a value for one of the variables to fill into the next substitution:

which simplifies down to

a + b = -11

Now for the 3rd and last coordinate:

which simplifies down to

4a + 2b = -20

Put the 2 bold equations together as a system and solve for one variable or the other.  I chose to solve for b first, so in order to do that, I multiplied the first equation by a -4, giving me a new system:

 -4a  -  4b  =  44

  4a  +  2b  = -20

and

-2b = 24 so

b = -12. Now plug that back in and solve for a:

a - 12 = -11 so

a = 1.

Now we have the function:

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step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47