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mote1985 [20]
3 years ago
12

Find the domain and range?

Mathematics
1 answer:
Nostrana [21]3 years ago
7 0
What do u want to find the domain and range of?
You might be interested in
Y=-3x^2-6x+24
Lera25 [3.4K]
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.

y=-3x^2-6x+24 \\ 0=-3x^2-6x+24

Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.

0=-3x^2-12x+6x+24\\0=-3x(x+4)+6(x+4)\\0=(-3x+6)(x+4)

Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.

-3x+6 = 0
-3x = -6
x = 2

x+4 = 0
x = -4

Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.

Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.

y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24

What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.

y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27

Thus the vertex is (-1, 27)

The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)

As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)




3 0
3 years ago
Answer pleaseee!!! There is a screen shot attached!
anastassius [24]

Answer:

7/33 = 21 repeating and I'm pretty sure the question wants you to write it as an improper fraction. so your answer would be 40/33

Step-by-step explanation:

5 0
2 years ago
(10-4)+20 divided by 10?
Luba_88 [7]

Answer:

8

Step-by-step explanation:

(10-4)+20/20

6+20/10

6+2

8

6 0
2 years ago
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either
kompoz [17]

The Rome data center is best described by the mean. The New York data center is best described by the median. The third option C is correct.

<h3>The Mean and Median:</h3>

The mean of a data set is the average of all the terms in the data set. The median of a data set is the value of the midpoint term in the frequency distribution.

From the given information, the table can be better expressed as:

           High   Low   Q1     Q3    IQR   Median    Mean         σ

Rome   18         1        3       7        4         6.5        6.4           4.3

NY        14         1       4.5    8.5      4        5.5        6.1            3.2

  • From the data sets in the table, the distribution for Rome is not largely diverse, and there isn't much departure from the mean value. It indicates that in the data set of Rome families, no outliers have occurred.

  • In New York, the data indicate a distinct outlier for New York families in Q3. This is due to the fact that the gap is so large, the mean may not be a good choice for determining the measure of the central tendency.

Therefore, we can conclude that, the Rome data center is best described by the mean and the median will be utilized to determine the central tendency in New York.

Learn more about mean and median here:

brainly.com/question/14532771

4 0
2 years ago
488, 460, 520, 544, 535<br> What is the range of the data?
n200080 [17]

Answer:

84

Step-by-step explanation:

To find the range, find the difference between the largest value and the smallest value.

544 - 460 = 84

7 0
3 years ago
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