Question

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 1

The correct answer would be D.) f(x) -x^2-12x-36

Answer 2

ANSWER

The correct option is D.

Step-by-step explanation

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

`x = - 6`
Then it means the root

`x = - 6`
repeats itself 2 times.

In order words the root

`x = - 6`
has a multiplicity of 2.

We can therefore write the equation


`{(x + 6})^(2) = 0`

`(x + 6)(x + 6) = 0`


We expand these to obtain



`{x}^(2) + 6x + 6x + 36 = 0`




This implies that


`{x}^(2) + 12x + 36 = 0 - - - (1)`

When we multiply through equation one by

`- 1`

we obtain,

`- {x}^(2) - 12x - 36 - - (2)`


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


`f(x) = {x}^(2) + 12x + 36`

and


`f(x) = - {x}^(2) - 12x - 36`

respectively.

The above two parabolas have root

`x = - 6`
that does not cross the x-axis