Answer:

Step-by-step explanation:
We want to write the equation of a quadratic whose graph passes through (-3, 2), (-1, 0), and (1, 6). 
Remember that the standard quadratic function is given by: 

Since it passes through the point (-3, 2). This means that when  ,
,  . Hence:
. Hence: 

Simplify: 

Perform the same computations for the coordinates (-1, 0) and (1, 6). Therefore: 

And for (1, 6): 

So, we have a triple system of equations: 

We can solve this using elimination. 
Notice that the b term in Equation 2 and 3 are opposites. Hence, let's add them together. This yields: 

Compute: 

Let's divide both sides by 2: 

Now, let's eliminate b again but we will use Equation 1 and 2. 
Notice that if we multiply Equation 2 by -3, then the b terms will be opposites. So: 

Multiply: 

Add this to Equation 1: 

Compute: 

Again, we can divide both sides by 2: 

So, we know have two equations with only two variables: 

We can solve for a using elimination since the c term are opposites of each other. Add the two equations together: 

Compute: 

Solve for a: 

So, the value of a is 1. 
Using either of the two equations, we can now find c. Let's use the first one. Hence: 

Substitute 1 for a and solve for c: 

So, the value of c is 2. 
Finally, using any of the three original equations, solve for b: 
We can use Equation 3. Hence: 

Substitute in known values and solve for b: 

Therefore, a=1, b=3, and c=2. 
Hence, our quadratic function is: 
