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Answer:
.
Step-by-step explanation:
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:
.
Solve for :
.
Hence the equation for this parabola:
.