Question

PLEASE HELP FAST 100 POINTS!

Construct the graph of the following function and identify its zeros on the same document. f(x) = (-x + 2)(x + 1)(x +2). Upload your document in the box below.

Answer 1

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:

`{ - (1)/(3) - ( √(13) )/(3) - (1)/(3) + ( √(13) )/(3) }`

decreasing interval:

`( - \infty - (1)/(3) - ( √(13) )/(3) )( - (1)/(3) + ( √(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`

Answer 2

Given function:

• f(x) = (-x + 2)(x + 1)(x +2)

We can rewrite it as:

• f(x) = - (x - 2)(x + 1)(x +2)

Zeros are:

• - (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.

Considering the above two factors we can define the shape of the graph:

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

See the graph and zero's reflected.