SOLUTION: Find the equation of the quadratic function with roots -8 and -6, "a" less than zero, and a vertex at (-7, 2).

Question 716254: Find the equation of the quadratic function with roots -8 and -6, "a" less than zero, and a vertex at (-7, 2).
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
When a number is a root of a polynomial function then (x - that number) is a factor of that function. So the quadratic function you are looking for, in factored form, will be:

In general, the "a" can be any non-zero number. But the problem states that "a" should be less than zero (or negative) and that we must have a vertex at (-7, 2). So there will probably be only one value for "a" that will fit. First we will multiply out the factors. Using FOIL on the last two factors:

Distributing the "a":

Now we set out to figure out what "a" must be. The vertex, (-7, 2), should fit this equation and we can use this to find "a". Substituting -7 for x and 2 for y/f(x) we get:

Now we solve for "a". We start by simplifying...

Dividing by -1:

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