Jijsome1t9exxi
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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

Respuesta :

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

The correct option is D.

EXPLANATION

If the parabola touches but does not cross the x-axis at
[tex]x = - 6[/tex]
Then it means the root
[tex]x = - 6[/tex]
repeats itself 2 times.

In order words the root
[tex]x = - 6[/tex]
has a multiplicity of 2.

We can therefore write the equation

[tex] {(x + 6})^{2} = 0[/tex]
[tex](x + 6)(x + 6) = 0[/tex]


We expand these to obtain


[tex] {x}^{2} + 6x + 6x + 36 = 0[/tex]




This implies that

[tex]{x}^{2} + 12x + 36 = 0 - - - (1)[/tex]

When we multiply through equation one by
[tex] - 1[/tex]

we obtain,
[tex] - {x}^{2} - 12x - 36 - - (2)[/tex]


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

[tex]f(x) = {x}^{2} + 12x + 36[/tex]

and

[tex]f(x) = - {x}^{2} - 12x - 36[/tex]

respectively.

The above two parabolas have root
[tex]x = - 6[/tex]
that does not cross the x-axis

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