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

ANSWER

The correct option is D.

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

Answer 2

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