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Kay [80]
3 years ago
13

Find f(-2) if f(x)=4x^2+3x-5

Mathematics
1 answer:
valentina_108 [34]3 years ago
3 0

Answer:

f(-2) = 5

Step-by-step explanation:

To find f(-2), plug in -2 wherever there is an x.

f(x) = 4x² + 3x - 5

f(-2) = 4(-2)² + 3(-2) - 5

f(-2) = 4(4) + 3(-2) - 5

f(-2) = 16 - 6 - 5

f(-2) = 10 - 5

f(-2) = 5

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Pls someone help me figure out how to do this!
Dafna11 [192]

Answer:

  g(x) = -3/5|x -6| +4

Step-by-step explanation:

Given the graph of an absolute value function, you want the equation for it.

<h3>Transformations</h3>

The desired form is ...

  g(x) = a|x -h| +k

The parameters a, h, k represent different features of the transformation of the graph of the parent function f(x) = |x|.

<h3>Vertical scale factor</h3>

The parameter 'a' is the vertical scale factor. There are two features of this graph that tell you what the value is.

  • the slope of the lines
  • the direction of opening

The line on the left side of the vertex seems to intersect points (1, 1) and (6, 4). The slope of this line can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (4 -1)/(6 -1) = 3/5

The graph opens downward, meaning that the parent absolute value function has been reflected across the x-axis. In other words, the sign of 'a' is negative. Its magnitude is the slope we just found, so ...

  • a = -3/5

<h3>Translation</h3>

When a function is translated h units horizontally and k units upward, the transformed function becomes ...

  g(x) = f(x -h) +k

We notice the vertex of the graph has moved from (0, 0) to (6, 4), so we have ...

  • h = 6
  • k = 4

<h3>Equation</h3>

Now that we know the values of the parameters in the equation, we can write it as ...

  g(x)=a|x-h|+k\\\\\boxed{g(x)=-\dfrac{3}{5}|x-6|+4}

__

<em>Additional comment</em>

Finding the vertical scale factor will work differently for different kinds of functions. In general, you want to find some vertical feature of the original function that you can recognize in the transformed function.

Here, that "feature" is the fact that an absolute value function has a rise of 1 for each run of 1 (a slope of 1) to the right of the vertex. This graph has a "rise" of -3 for a run of 5 to the right of the vertex. Effectively, the graph of the original absolute value function has been scaled by a factor of -3/5.

6 0
8 months ago
Solve the following equation for x: 6x-16=14
Ivenika [448]

To solve the equation for x, first, we add 16 from both sides of the equation:

\begin{gathered} 6x-16+16=14+16, \\ 6x=30. \end{gathered}

Now, we divide by 6:

\frac{6x}{6}=\frac{30}{6}.

Finally, we get that:

x=5.

Answer:

x=5.

8 0
1 year ago
What percent of 15% of 60
AveGali [126]

Answer:

the answer is 9

Step-by-step explanation:

15/100 ?/60

multiply 60 by 15 to get 900, the divide 900 by 100 to get <em>9</em>

4 0
2 years ago
If y=5x-3and 3x-y=-1, what is the value of y?<br> A. 7<br> B. -1<br> C. 2<br> D. -8
Genrish500 [490]
Ummm explain the question more but b seems to make the most sense
8 0
3 years ago
What are the next three terms in the sequence 4,8,12,16?
Mariana [72]

Answer:

20,24,28

Step-by-step explanation:

It is increasing by 4 each time

Mark me brainliest please :)

7 0
3 years ago
Read 2 more answers
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