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Alecsey [184]
1 year ago
5

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Mathematics
1 answer:
madam [21]1 year ago
8 0

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

<h3>Which statements are true?</h3>

Here we have the quadratic function:

f(x) = -x^2 - 4x + 5

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

f(x) = -x^2 - 4x + 5

So the vertex is at:

x = 4/(2*-1) = -2\\

Then the y-value of the vertex is:

f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

If you want to learn more about quadratic functions:

brainly.com/question/1214333

#SPJ1

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The answer should be 7x+28
I Hope this Helps!
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3 years ago
Find the value of this expression if x=1 and y=-5 <br> x^2y/7
AlekseyPX

Answer:

5/7

Step-by-step explanation:

8 0
2 years ago
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Graph the function y = 2x3 – x2 – 4x + 5. To the nearest tenth, over which interval is the function decreasing?
daser333 [38]
As you progress in math, it will become increasingly important that you know how to express exponentiation properly.

y = 2x3 – x2 – 4x + 5  should be written    <span>y = 2^x3 – x^2 – 4^x + 5.  The 
" ^ " symbol denotes exponentiation.

I see you're apparently in middle school.  Is that so?  If so, are you taking calculus already?  If so, nice!

Case 1:  You do not yet know calculus and have not differentiated or found critical values.  Sketch the function          </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5).  Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?

Case 2:  You do know differentiation, critical values and the first derivative test.  Differentiate  y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:

dy/dx = 6x^2 - 2x - 4 = 0.  Reduce this by dividing all terms by 2:

dy/dx = 3x^2 - x - 2 = 0    I used synthetic div. to determine that one root is x = 2/3.  Try it yourself.  This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1.  Again, you should check this.

Now we have 2 roots:  -1 and 2/3

Draw a number line.  Locate the origin (0,0).  Plot the points (-1, 0) and (2/3, 0).  This subdivides the number line into 3 subintervals:

(-infinity, -1), (-1, 2/3) and (2/3, infinity).

Choose a test number from each interval and subst. it for x in the derivative formula above.  If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.

Ask all the questions you want, if this explanation is not sufficiently clear.

4 0
3 years ago
Read 2 more answers
I need a little help :)
Naily [24]

So firstly, square root 9a^2 and 49: 3a+7\sqrt{b}-a+\sqrt{b}


Next, combine like terms, and your answer will be 2a+8\sqrt{b} , or the third option.

3 0
3 years ago
??????????????????????
gtnhenbr [62]

Answer:

110 degrees

Step-by-step explanation:

I don't know if that is correct.

6 0
3 years ago
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