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denis23 [38]
3 years ago
9

PLEASE HELP FAST 100 POINTS!

Mathematics
2 answers:
Ivahew [28]3 years ago
6 0

Answer:

<u>Given function:</u>

  • f(x) = (-x + 2)(x + 1)(x +2)

<u>We can rewrite it as:</u>

  • f(x) = - (x - 2)(x + 1)(x +2)

<u>Zeros are:</u>

  • - (x - 2)(x + 1)(x +2) = 0
  • x - 2 = 0 ⇒ x = 2
  • x + 1 = 0 ⇒ x = -1
  • x + 2 = 0 ⇒ x = -2

As leading coefficient is negative the function is decreasing.

As the function is of degree 3, it is odd.

<u>Considering the above two factors we can define the shape of the graph:</u>

  • It is decreasing function with one local minimum and one local maximum.

<em>See the graph and zero's reflected.</em>

Studentka2010 [4]3 years ago
4 0

Analyze the function:

f(x) =  \\ ( - x + 2)(x + 1)(x + 2)

Write properties of function:

Solution:

x-intercept/zero

{x}^{1}  =  - 2 \\  {x}^{2}  =  - 1 \\  {x}^{3}  = 2

y-intercept:

y = 4

domain:

( -  \infty  \: . \:  +  \infty )

type of function:

cubic \: function

standard form:

f(x) =  -  {x}^{3}  -  {x}^{2}  + 4x + 4

factorized form:

f(x) =  - ( - (x + 1)( x + 2) ( - 2x + 2))

even/odd:

neither

bounce/cross x-axis:

x =  - 2 \: . \: cross \: . \: x =  - 1 \: . \: cross \: . \: x = 2 \: . \: cross

increasing interval:

{ -  \frac{1}{3}  -  \frac{ \sqrt{13} }{3}  -  \frac{1}{3}  +  \frac{ \sqrt{13} }{3} }

decreasing interval:

( -  \infty  -  \frac{1}{3}  -  \frac{ \sqrt{13} }{3} )( -  \frac{1}{3}  +  \frac{ \sqrt{13} }{3}  \infty )

number of possibles real zero:

3

number of possible turning points:

2

order/degree:

3

leading term:

-  {x}^{3}

leading coefficient:

- 1

constant terms:

- 1

end behavior:

as \: x +  \infty  \: f(x) -  \infty  \\ as \: x -  \infty f(x) \infty

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