I am giving 15 points
Write the quadratic equation in a standard form that represents the table below:

X Values are: -2, -1, 0, 1 and Y Values are: 12, 6, 2, 0

f(x)=

Step-by-step explanation:

I used 3 of the coordinates to solve for the a, b, and c that we need in

We have 3 unknowns so we need 3 equations.  The coordinates I used are from your table:

(-2, 12), (-1, 6), (0, 2).  Start with (0, 2).  Sub in a 2 for y and a 0 for x in the standard form of the quadratic:

which simplifies very nicely to

c = 2.  We will use that value now when we do this again using (-2, 12):

 and

12 = 4a - 2b + 2 and

4a - 2b = 10 (1)

Do it again with the third coordinate (-1, 6):

and

6 = 1a - b + 2 and

a - b = 4 (2)

Now we have a system of equations, (1) and (2) that we will combine and solve for a:

 4a  -  2b  =  10

   a   -   b   =   4

Multiply the second equation by -2 to get a new system:

 4a  -  2b  =  10

-2a  +  2b = -8

Add to get

2a = 2 so

a = 1

Now sub in 1 for a in (2):

1 - b = 4 and

-b = 3 so

b = -3

Now we have all that we need to write the equation:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt