Determine the equation of the parabola passing through the points (-3,13), (0,1), and (1, -7)

Step-by-step explanation:

You need to do some solving simultaneously to get these values.  Your quadratic equation is of the form

Use the coordinates you've been given to solve 3 equations.  It will be super simple if we start with the coordinate (0, 1).  Here's why (obvious after some substitution is done):

which gives us that

c = 1.  Now we have a variable to plug in for c to solve for a and b.  Again, we have coordinates that we can use to create 2 more equations:

and, simplified:

9a - 3b = 12

and the second equation is:

and, simplified:

a + b = -8

Now combine the 2 bold equations and solve by elimination or substitution to find either a or b.  I chose elimination and multiplied the second equation by 3 to get a new equation:

3a + 3b = -24

Using the elimination method:

9a - 3b = 12

3a + 3b = -24

You can see that the b's subtract each other away, leaving us with

12a = -12 so

a = -1

Now plug -1 in for a to solve for b:

-1 + b = -8 so

b = -7 and the quadratic is