Parabola problem

Question

Find an equation of the form
y = a(x − x₁)(x − x₂) of a parabola with a point of (5,-5) and x-intercepts of -4 and 6.

Answer 1

Cool.  So to put a parabolic equation into factored form like this, first find the factors.  the factors come from the opposites of the x-intercepts.  In this example, (x+4) and (x-6)

 

So, our equation looks like this, y = a(x+4)(x-6)

 

Now we plug in the point (5,-5) to find a.

 

so, -5 = a(5+4)(5-6)

 

-5 = a(9)(-1)

 

-5 = -9a

 

a = 5/9

 

the final equation is y = (5/9)(x+4)(x-6)