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spin [16.1K]
3 years ago
12

Find the equation for the parabola that passes through the point (-2,-4), with vertex at (3,1) and a vertical axis

Mathematics
1 answer:
Igoryamba3 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1), hence

y = a(x - 3)² + 1

To find a substitute (- 2, - 4) into the equation

- 4 = a(- 2 - 3)² + 1

- 4 = 25a + 1 ( subtract 1 from both sides )

25a = - 5 ( divide both sides by 25 )

a = - \frac{5}{25} = - \frac{1}{5}

y = - \frac{1}{5} (x - 3)² + 1 ← in vertex form

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Express this to single logarithm
zzz [600]

Answer:  \log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right)

We have something in the form log(x/y) where x = q^2*sqrt(m) and y = n^3. The log is base 2.

===========================================================

Explanation:

It seems strange how the first two logs you wrote are base 2, but the third one is not. I'll assume that you meant to say it's also base 2. Because base 2 is fundamental to computing, logs of this nature are often referred to as binary logarithms.

I'm going to use these three log rules, which apply to any base.

  1. log(A) + log(B) = log(A*B)
  2. log(A) - log(B) = log(A/B)
  3. B*log(A) = log(A^B)

From there, we can then say the following:

\frac{1}{2}\log_{2}\left(m\right)-3\log_{2}\left(n\right)+2\log_{2}\left(q\right)\\\\\log_{2}\left(m^{1/2}\right)-\log_{2}\left(n^3\right)+\log_{2}\left(q^2\right) \ \text{ .... use log rule 3}\\\\\log_{2}\left(\sqrt{m}\right)+\log_{2}\left(q^2\right)-\log_{2}\left(n^3\right)\\\\\log_{2}\left(\sqrt{m}*q^2\right)-\log_{2}\left(n^3\right) \ \text{ .... use log rule 1}\\\\\log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right) \ \text{ .... use log rule 2}

8 0
3 years ago
#1.) Which of the numbers below belong to the solution x-4≥5?
jekas [21]
The answer is C 
9 - 4 = 5
5 is equal to 5

13 - 4 = 9
9 is greater than 5

The symbol means greater than or equal to 
6 0
3 years ago
95 - 4G < 40 + 5G plz help me
7nadin3 [17]

This answer would be (55/9, ∞)

5 0
3 years ago
Someone help me in this algebra question please 100% correct only
Karo-lina-s [1.5K]
B
5/4 times 4/5X=8/1 times 5/4
X=40/4
X=10
8 0
3 years ago
Y=_x+4<br> x + 2y =<br> 8<br> How many solutions dose this linear system have
jeyben [28]

Answer:

X=-1, y=4

Step-by-step explanation:

y = x + 4 \\ x + 2y = 8 \\  =  =  =  =  =  =  =  =  =  =  =  = \\ y - x = 4 \\ x + 2y = 8

by using eliminating property

3y = 12 \\ y = \frac{12}{3}    = 4

by substitution

X=-1

6 0
3 years ago
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