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Artist 52 [7]
2 years ago
14

Pls help !!! find the rate of change on [-1, 4]

Mathematics
1 answer:
pochemuha2 years ago
4 0

Answer:

Step-by-step explanation:

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What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2, –14)?
vichka [17]

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a  =  determines whether the graph opens up or down, and it also makes the parent function <u>wider</u> or <u>narrower</u>.

  • <u>positive</u> value of a = opens <u><em>upward</em></u>
  • <u>negative</u> value of a = opens <u><em>downward</em></u>
  • a is between 0 and 1, (0 < a < 1) the graph is <u><em>wider</em></u> than the parent function.
  • a > 1, the graph is <u><em>narrower</em></u> than the parent function.

<em>h </em>=<em> </em>determines how far left or right the parent function is translated.

  • h = positive, the function is translated <em>h</em> units to the right.
  • h = negative, the function is translated |<em>h</em>| units to the left.

<em>k</em> determines how far up or down the parent function is translated.

  • k = positive: translate <em>k</em> units <u><em>up</em></u>.
  • k = negative, translate <em>k</em> units <u><em>down</em></u>.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)²  -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)

8 0
2 years ago
It takes Engineer Kweku three hours to drive to his brother’s house at an average speed of 50 miles per hour. If He takes the sa
11Alexandr11 [23.1K]

Answer:

  2.5 hours

Step-by-step explanation:

The product of speed and time is distance. If the distance is the same, then time is inversely proportional to speed. At 60/50 = 6/5 times the speed, the return trip will take 5/6 times the time:

  (5/6)(3 hours) = 2.5 hours . . . time for return trip

5 0
2 years ago
You have a standard deck of cards. what are the chances that you get a king. Answer in a percent
fenix001 [56]

Answer:

5%

Step-by-step explanation:

3 0
2 years ago
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HELP: Cho charges $1500 to build a small deck and $2500 to build a large deck. During the spring and summer, she built 5 more sm
Ludmilka [50]

Answer:

if she build x numbers of large decks, therefore small decks would be (x + 5)

1500*(x+5)+2500x   =23500

1500x+7500+2500x=23500

4000x+7500             =23500

                        4000x=23500-7500

                         4000x=16000

                                  x=4

4+5=9

cho built 4 large decks and 9 small decks

7 0
3 years ago
The figure below shows a rectangular prism and a cube: A rectangular prism and a cube are drawn side by side. The length of the
cluponka [151]
5 in.*.8 in*1.6 in =6.4 in^3 (Volume of rectangular prism)
.2^3=0.008 in^3 (Volume of cube)
6.4/0.008=800
so basically the answer is 800 cubes
7 0
2 years ago
Read 2 more answers
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