Question

What is the equation, in the form y= x^2 + bx + c of the parabola which passes through the points (-3,0) and (1,-16)?

y=a(x-s)(x-q)
y=a(x-(-3))(x-1)
y=a(x+3)(x-1)
y=a(x^2+2x-3)
I'm confused...

Answer 1

Since the coefficient of x^2 is 1, a=1. The point (-3,0) means that -3 is a root of the function. So,

y = (x+3)(x-q)

y(3) = -16, so
(6)(3-q) = -16
3-q = -8/3
q = 17/3

Now we know that

y = (x+3)(x-17/3)

That fits any of the choices, given the proper value of a.

I suspect that you should have started out with

y = ax^2+bx+c

In that case, any of the given forms will work, since two points do not pin down the function. There are infinitely many parabolas which go through (almost) any two given points.