Consider function f.

Mathematics

1 answer:

MariettaO [177]3 years ago

4 0

Answer:

x = 2, x = -1, x = -3

As x approaches negative infinity, f(x) approaches negative infinity

Step-by-step explanation:

Given function

f(x)= x^3 + 2x^2 - 5x - 6

Finding zero's

x^3 + 2x^2 - 5x - 6 = 0
x^3 - 2x^2 + 4x^2 - 8x +3x - 6 =
(x - 2)(x^2 + 4x + 3) =
(x - 2)(x^2 + x + 3x + 3) =
(x - 2)(x(x + 1) + 3(x + 3)) =
(x - 2)(x + 1)(x + 3)

Zero's are

x = 2, x = -1, x = -3

See the graph attached

Correct end behavior as per graph:

As x approaches negative infinity, f(x) approaches negative infinity

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Answer:

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Answer:

See explanation

Step-by-step explanation:

1. Factor the function $f(x)=-2x^2+16x-30:$

$f(x)=-2x^2+16x-30=-2x^2+6x+10x-30=-2x(x-3)+10(x-3)=-2(x-3)(x-5).$

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3. Find the vertex:

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