PLEASE HELP
Write the quadratic equation in standard form that represents the table below:
x y

-2 19

-1 12

0 7

1 4

f(x)=

Step-by-step explanation:

You have 3 unknowns: a, b, and c.  It's our job to find them algebraically.  I'm going to start with the point where x = 0 and y = 7.  You'll see why in a minute.  Filling in the standard form of a quadratic

 using (0, 7):

 gives you that c = 7.  We will use that value now when we write the next 2 equations.  Now the point (-2, 19):

 and

so

12 = 4a - 2b

Now for the next point (-1, 12):

 and

 so

5 = a - b

Now we have a system of equations (the 2 bold font equations) that we will solve by elimination:

 12  =  4a  -  2b

  5  =   a   -    b

Multiply the bottom equation by -4 to get a new system:

 12  =  4a  -  2b

-20  = -4a  +  4b

Add those together to get rid of the a terms and end up with

-8 = 2b so

b = -4

Now we can sub in -4 for b to solve for a.  I'm using the second bold type equation to do this:

5 = a - (-4) and

5 = a + 4 so

a = 1 and the equation for the quadratic function is

yes

step-by-step explanation: