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Romashka-Z-Leto [24]
3 years ago
8

Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (0, 0) and has (-3, -6) as its vertex. What

is the standard form of the equation?
Mathematics
1 answer:
Arisa [49]3 years ago
6 0
F(x) = a(x-h)²<span> + k

</span><span><u>Given that the vertex is (-3 -6):</u>

</span>f(x) = a(x + 3)² -6
<span>
<u>Given that it passes through (0.0), find a:</u>

a(0 + 3)</span>² - 6 = 0
<span>
9a - 6 = 0

9a = 6

a = 6/9 =2/3

<u>So the equation is :</u>

</span>f(x) = 2/3(x + 3)² -6
<span>
<u>Write the equation in standard form:</u>

</span>f(x) = 2/3(x² + 6x + 9) - 6

f(x) = 2/3x² + 4x + 6 - 6

f(x) = 2/3x² + 4x
<span>
Answer: </span>f(x) = 2/3x² + 4x<span>


</span>
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Change the x and y
Then solve for y
X= 8y+1
Subtract 1 from both sides
X-1=8y
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4 0
3 years ago
K +-23 = -100<br>help me
Alex_Xolod [135]

Answer:

-77

Step-by-step explanation:

-77 + -23 = -100

4 0
3 years ago
Write the standard equation of the circle with the given center and passes through the given point. Center (7,-2); Point= (1,-6)
vodomira [7]

Answer:

(x - 7)² + (y + 2)² = (2√13)²

Step-by-step explanation:

We already know that the center is at (7, -2), but must find the radius.  The radius is the distance between the points (7, -2) and (1, -6):

r = √ [6² + 4²] ) = √(36 + 16) = √52 = √4√13 = 2√13.

Then the desired equation is (x - 7)² + (y + 2)² = (2√13)²

6 0
3 years ago
A scientist runs an experiment involving a culture of bacteria. She notices that the mass of the bacteria in the culture increas
Genrish500 [490]

The growth factor for the mass of bacteria is 2.8 in 1 week.

Step-by-step explanation:

Step 1:

It is given that the bacteria in the culture increase by 260% per week. Now we assign values to get a better understanding. If there were 1,000 bacteria in the culture at the start of the week there would be 1,000 + 260% at the week's end = 1,000 + 2,600 = 3,600 at the week's end.

Step 2:

To calculate the growth factor, we calculate the difference between the present value and the past value and divide it by the past value.

Here the past value is 1,000 and the present value is 2,600.

Growth factor = \frac{difference in values}{past value} = \frac{3,600-1,000}{1000} = \frac{2,600}{1,000} = 2.6.

So the growth factor is 2.6 per week.

7 0
3 years ago
How many different three digit numbers can be made with 123456789
FinnZ [79.3K]

Answer:

84

Step-by-step explanation:

Since, the digit should be in ascending order, therefore we have to group 123456789 into 3–3 groups with its digits being in ascending order.

<em>Step 1:</em>

Select 1 as one digit

<em>Step 2:</em>

Select 2 as a 2nd digit.

<em>Step 3: </em>

We have 7 numbers (3,4,5,6,7,8,9) as a 3rd digit of a 3-digit number. Therefore, We have 7 numbers in the form of 12_.

Go back to Step 2 and Select 3 as a 2nd digit. Then, we have 6 numbers (4,5,6,7,8,9) as a 3rd digit of the form 13_.

Continue these steps till you get the number of 3-digit numbers in the form of 1__ to 189 which will be 28 numbers.

Go back to Step 1 now and select 2 as a 1st digit and in Step 2, start with 3 as a 2nd digit.

In step 3, you’ll have 6 numbers (4,5,6,7,8,9) as a 3rd digit of the form 23_.

Continue these steps till you find the number of the 3 digit number of the form 2__ to 289 which will be 21

Repeat the steps again to find the number of 3digit number of the form 3__ to 389 which will be 15.

Then find 4__ to 489, 5__ to 589, ……till 789

the answers will be like this

1__=28

2__=21

3__=15

4__=10

5__=6

6__=3

789 which is 1

Adding all these, you’ll get 84.

4 0
2 years ago
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