The zeros of a parabola are –4 and 2, and (6, 10) is a point on the graph. Which equation can be solved to determine the value of a in the equation of the parabola?

Answer 1

You can turn a "zero" into a "factor" of a polynomial by just adding "x -" in front of the zero. So for the zero "-4", the corresponding factor is (x - -4) which is the same as (x + 4). For the zero "2", the corresponding factor is (x - 2). So the polynomial the has zeros -4 and 2 can be written as (x + 4)(x - 2)

HOWEVER, there can be an infinite number of POSSIBLE parabolas that have those zeros because you can put a multiplier in front of (x + 4)(x - 2) such as 2(x + 4)(x - 2) or 3(x + 4)(x - 2) or 4(x + 4)(x - 2) or . . .

To determine exactly which one this parabola is, we can write it as y = a(x + 4)(x - 2) then we can plug in the point (6, 10) as the (x, y) and solve for "a":

10 = a(6 + 4)(6 - 2)

10 = a(10)(4)

10 = 40a

a = 1/4

So the polynomial is y = 1/4(x + 4)(x - 2)