Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. which function could heather be writing? a. f(x) = x2 36x 12 b. f(x) = x2 – 36x – 12 c. f(x) = –x2 12x 36 d. f(x) = –x2 – 12x – 36

ANSWER

The correct option is D.

EXPLANATION

If the parabola touches but does not cross the x-axis at

Then it means the root

repeats itself 2 times.

In order words the root

has a multiplicity of 2.

We can therefore write the equation




We expand these to obtain



This implies that



When we multiply through equation one by


we obtain,


The functions that corresponds to equation (1) and (2) are:



and



respectively.

The above two parabolas have root

that does not cross the x-axis