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3 years ago

What is f(x) = 7x2 + 42x written in vertex form?

Mathematics

1 answer:

Serggg [28]3 years ago

6 0

F(x)= 7 x² + 42 x = 7 ( x² + 6 x ) = 7 ( ( x² + 6 x + 9 ) - 9 ) =
= 7 ( x + 3 )² - 63 (vertex form)
Answer: D)

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Sketch a graph of the polynomial function f(x) =x3− 2x2. Use it to complete the following:

AlladinOne [14]

Answer:

We have the function:

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

To sketch this, we need to graph some points, and then just draw a line that passes through the points.

The graph of this equation is shown below.

Now we can complete the question.

If the graph is below the x-axis in some interval, the function is negative in that interval

If the graph is above the x-axis in some interval, the function is positive in that interval.

If the graph goes up in a interval, then the function is increasing in that interval

If the graph goes down on an interval, then the function is decreasing in that interval.

Then:

1) f is------ on the intervals (−∞, 0) and (0, 2).

Here we can see that the graph is below the x-axis in those intervals, then here we have:

f is negative on the intervals (−∞, 0) and (0, 2).

2) f is------ on the interval (2,∞)

Here the answer is positive:

f is positive on the interval (2,∞)

3) fi is ------ on the interval (0, 4/3)

In the graph, you can see that the graph goes down in that interval, then the correct answer here is:

f is decreasing on the interval (0, 4/3)

4) f is------ on the intervals (−∞, 0) and (4/3, ∞).

In this case, we can see that the graph goes up in these intervals, then the correct answer here is:

f is increasing on the intervals (−∞, 0) and (4/3, ∞).

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Which is the graph of f(x) = -(x + 3)(x + 1)?

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Answer:

See attachment

Step-by-step explanation:

A function is given to us and we need to tell which graph represents the given function. The function given to us is,

$\tt: \implies f(x) = -( x + 3 )( x + 1 )$

Let's find out at which points do the graph Intersects x axis / finding the roots. For that substitute f(x) = 0 , we have ,

$\tt: \implies -(x +3)( x + 1 ) = 0$

Equate each factor by 0 ,

$\tt: \implies \boxed{\blue{ \tt x = -1,-3 }}$

Therefore the graph will intersect x axis at x is equal to -1 and x is equal to -3 .

On looking at the given graphs in the options the second graph intersects x axis at -1 and -3 .

Hence the second option is correct . 

{ See attachment }

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Step-by-step explanation:

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