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Firdavs [7]
3 years ago
8

Which of the following equations is of a parabola with a vertex at (0, -5)

Mathematics
2 answers:
AnnyKZ [126]3 years ago
6 0

Answer:

Equation of parabola is y = x² - 5 .

Step-by-step explanation:

Given  : parabola with a vertex at (0, -5).

To find :  which of the following equations is of a parabola.

Solution : We have given  vertex at (0, -5).

Vertex form of parabola   y = a(x - h)² + k .

Where (h ,k ) is vertex

We have h = 0 , k = -5 .

Equation : y = 1(x - 0)² - 5

y = x² - 5 .

Therefore, Equation of parabola is y = x² - 5 .

Harlamova29_29 [7]3 years ago
4 0

The x, which is zero in this case will always be the number that goes on the inside of the equation, so far you have y=(x+0)^2 or y=x^2.

The y, which is negative will go on the end of the equation. So you get y=x^2-5

The equation is y=x^2-5 or C if it is multiple choice

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2 years ago
Here are some values of sequence Q. Write a recursive definition for the sequence.
Rashid [163]

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

4 0
3 years ago
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