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3 years ago

Find all x and y intercepts of the graph of the function f(x)= 2x^3+6x^2-2x-6

Mathematics

1 answer:

topjm [15]3 years ago

4 0

9514 1404 393

Answer:

y-intercept: (0, -6)
x-intercepts: (-3, 0), (-1, 0), (1, 0)

Step-by-step explanation:

We notice the first pair of coefficients is the same as the last pair (with the sign changed). This means we can factor by grouping.

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

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

f(x) = 2(x^2 -1)(x +3) = 2(x -1)(x +1)(x +3)

The factors are made to be zero when x is 1, -1, or -3.

The x-intercepts are (1, 0), (-1, 0), (-3, 0).

The y-intercept is the constant, -6.

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Step-by-step explanation:

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3 years ago

{(7,4),(6,3),(5,3)} function? Explain

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3 years ago

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inna [77]

Circumference is found with the formula

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3 years ago

Activity

hodyreva [135]

Answer:

The answers to each part are:

Part A.

The quantity of apples is one-third of the quantity of grapes.

Part B.

The quantity of apples is a quarter of the quantity of strawberries.

Part C.

The number of cherries is two-elevenths of the total fruit.

Step-by-step explanation:

To identify the answer in each case, you must remember that all the parts are equal, then:

Part A.

The parts of apples are 1 and the parts grapes are 3, so if you divide the first quantity with the second quantity you obtain:

1 / 3 = 1/3 (one-third)

So, the quantity of apples is one-third of the quantity of grapes or the quantity of apples is three times smaller than the quantity of grapes.

Part B.

The parts of apples are 1 and the parts of strawberries are 4, then you must divide the first quantity with the second quantity:

1 / 4 = 1/4 (a quarter)

In this case, the quantity of apples is a quarter of the quantity of strawberries or the quantity of apples is four times smaller than the quantity of strawberries.

Part C.

First, you must add all the part of fruit:

1 part apple
1 part orange
4 parts strawberry
2 parts cherry
3 parts grape

The total of fruits is 11 parts, taking into account the quantity of cherries is 2, now you can divide the number of cherries with the total parts of fruit:

2 / 11 = 2/11 (two-elevenths)

Now, you can see the number of cherries is two-elevenths of the total fruit.

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3 years ago

What is the derivative of g(x)=e^(x^2+2x)+3x

UNO [17]

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7 0

3 years ago

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