Whole numbers are the set of numbers that include zero and all the positive numbers that we count with, like 0, 1, 2, 3, 4, 5, etc. What this set doesn't include are negative numbers and numbers that are expressed as fractions or decimals. In other words, whole numbers include zero and all positive integers.
Start with the two -intercepts. The two zeros of the quadratic equation for this parabola are:
, and
.
(These are the -coordinates of the two -intercepts.)
By the factor theorem, (where is a real number) is a zero of a polynomial if and only if is a factor of that polynomial.
A quadratic equation is also a polynomial. In this case, the two zeros would correspond to the two factors
.
A parabola could only have up to two factors. As a result, the power of these two factor should both be one. Hence, the equation for the parabola would be in the form
,
where is the leading coefficient that still needs to be found. Calculate the value of using the -intercept of this parabola. (Any other point on this parabola that is not one of the two -intercepts would work.)
Since the coordinates of the -intercept are , and . The equation becomes: