A parabola is defined by the equation (x − 5)2 = 12(y + 2). In which direction will the parabola open?

QUESTION POSTED AT 18/01/2020 - 07:19 AM

Answered by admin AT 18/01/2020 - 07:19 AM

Since the equation is in the form:
(1/a)(y – k) = (x – h)2


Then, the parabola will open either upward or downward. To tell which direction will the parabola open, the coefficient of the term:

(y – k)
must be inspected.

The coefficient is 12 and it is a positive number, therefore, the parabola will open upward.

Post your answer

Related questions

Expand and simplify (x+9)^2

1) x^2 + 2x * 9 + 9^2
2) x^2 + 2x + 81
3) x^2 + 18 +81

ANSWERED AT 21/02/2020 - 12:05 PM


QUESTION POSTED AT 21/02/2020 - 12:05 PM

What is y+5=7(x+1) in standard form?

Y=7x+2 
This is your answer hope this helps :)

ANSWERED AT 21/02/2020 - 11:39 AM


QUESTION POSTED AT 21/02/2020 - 11:39 AM

HELP PLEASE? Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the exponential function relating time and money? The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time. The initial value of the graph is 200. The graph increases by a factor of 5 per 1 unit increase in time. The initial value of the graph is 500. The graph increases by a factor of 2 per 1 unit increase in time. The initial value of the graph is 500. The graph increases by a factor of 1.02 per 1 unit increase in time.

I know that just the answer is not enough. You need to understand why and how. So I will explaing the steps.

First you need to state the equation that represents the function.

Investment is $200 and interest rate is 5%, y is the amount of money after x periods.

Note that after 1 period the amount of money is 200 plus 5% interest, which is 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)

After 2 periods the amount is 200(1.05)*(1.05) = 200 (1.05)^2

After 3 periods the amount is 200 (1.05)^3

And now you can deduce that after x periods y = 200 (1.05)^x

You can then analyze the function to predict the shape and critical points of the graph.

The answers are based in the initial value and the increasing factor.

The initial value is when x = 0, which yields to y = 200 (1.05)^0 = 200*1 = 200

And the increasing factor is 1.05 because any value is the previos one times 1.05.

Then the answer is the first option. The initial value is 200 and the graph increases by a factor of 1.05 per 1 unit increase in time. 

ANSWERED AT 21/02/2020 - 11:37 AM


QUESTION POSTED AT 21/02/2020 - 11:37 AM

Can someone please help me with this question! btw thx in advance. Use the remainder Theorem to find the remainder: (x^3-1)/(x-4)

F(x)/(x-a)=f(a)
Here a=4
So we need f(4)
F(4)=(4)^3 -1
F(4)=64-1=63

ANSWERED AT 21/02/2020 - 11:18 AM


QUESTION POSTED AT 21/02/2020 - 11:18 AM

What is the length of x


Immediate math help from PAID TUTORS. (paid link)Click here to see ALL problems on Triangles
  Question 118094: Find the length x in the triangle. Side 1=8. Side 2=x. Side 3=12 (Scroll Down for Answer!)Did you know that Algebra.Com has hundreds of free volunteer tutors who help people with math homework? Anyone can ask a math question, and most questions get answers!Check it Out!OR get immediate PAID help on:
Type Your Question Go!!! Answer by jim_thompson5910(34119) About Me  (Show Source):You can put this solution on YOUR website!I'm assuming that the triangle is a right triangle and that side 3 is the hypotenuse. 

We basically have this triangle set up: 
 Since we can see that the triangle has legs of 8 and x with a hypotenuse of 12, we can use Pythagoreans theorem to find the unknown side. 

Pythagoreans theorem: 
a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse 


8%5E2%2Bx%5E2=12%5E2 Plug in a=8, b=x, and c=12. Now lets solve for x 

6+4+%2B++x++%5E+2+=+1+4+4 Square each individual term 
 


+x++%5E+2+=+1+4+4+-+6+4 Subtract 64 from both sides 

+x++%5E+2+=+8+0 Combine like terms 

s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+8+0+%29 Take the square root of both sides 

x=4%2Asqrt%285%29 Simplify the square root 

Which approximates to... x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6 
So our answer is x+=+8+.+9+4+4+2+7+1+9+0+9+9+9+9+1+6....

ANSWERED AT 21/02/2020 - 10:59 AM


QUESTION POSTED AT 21/02/2020 - 10:59 AM

A 2 percent increase in the price of milk causes a 4 percent reduction in the quantity demanded of chocolate syrup. what is the cross-price elasticity of demand for chocolate syrup with respect to the price of milk?

The cross-price of elasticity of demand for chocolate syrup with respect to the price of milk would be :

e = % ΔQ chocolate syrup / %ΔP of milk

e = -4% / 2%

e = -2 % 

ANSWERED AT 21/02/2020 - 10:49 AM


QUESTION POSTED AT 21/02/2020 - 10:49 AM

Use substitution to solve each system. -3y = -2x - 1 y = x - 1

-3y = -2x - 1 

-3(x - 1) = -2x - 1 

-3x + 3 = -2x - 1 

-x + 3 = -1 

-x = -4

x = 4 
 
y = x - 1

y = (4) - 1 

y = 3

(4,3) is your solution



ANSWERED AT 21/02/2020 - 10:35 AM


QUESTION POSTED AT 21/02/2020 - 10:35 AM

I need help on 2 and 3

A then c ok so I think wait nope I'm right

ANSWERED AT 21/02/2020 - 09:42 AM


QUESTION POSTED AT 21/02/2020 - 09:42 AM

1.) what do values a h and k tell about the graph 2.) graph function 3.) state domain/range 4.) are there any intercepts? List all

Attached is a very useful chart for translations. [https://us-static.z-dn.net/files/df7/85ffaebe52d207009f6ed5967a5e05b4.jpg]

A number added or subtracted outside of parentheses shifts the graph vertically up (if number is added) or down (if number is subtracted).
As you can see in the chart,
f(x) + k shifts the graph up k units, and
f(x) - k shifts the graph down k units.

A number that is multiplied to x outside parentheses stretches or shrinks the graph vertically. If that number is greater than 1, then it stretches the graph. If the number is a fraction or between 0 and 1, then it shrinks the graph vertically.

As you can see in the chart,
a * f(x), where a>1 stretches the graph f(x) vertically by a factor a.
a * f(x), where a is between 0 and 1 shrinks the graph f(x) vertically by a factor of a.

When h is added or subtracated from x inside the parentheses, the graph is shifted horizontally right or left. Remember that this is opposite of what the sign is:
If h is positive, f(x + h), then the graph shifts left h units.
If h is negative, f(x - h), the graph shifts right h units.
Note that the attached chart uses c instead of h.

Since the function will be quadratic (degree is 2), the domain will be all real numbers, from -infinity to +infinity (-∞, +∞).
Depending on whether the value of a is positive or negative, the graph will open up like a U (if a is positive) or open down like an upside down U (if a is negative).

Since the equation is in vertex form f(x) = a(x - h)^2 = k, the vertex is (h, k). The range (set of y-values) will be from y-coordinate of the vertex (k) to positive or negative infinity depending on whether the graph opens up or down. 

ANSWERED AT 21/02/2020 - 09:41 AM


QUESTION POSTED AT 21/02/2020 - 09:41 AM

How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3? None One Two Infinitely many

Answer:

Option (d) is correct.

The equation 5x + 3(x − 1) = 10x − 2x − 3 will have infinite many solution.

Step-by-step explanation:

  Given : the equation 5x + 3(x − 1) = 10x − 2x − 3

We have to find the number of solution to the equation 5x + 3(x − 1) = 10x − 2x − 3

Consider the given equation 5x + 3(x − 1) = 10x − 2x − 3

This can be written as two equations as

y=5x + 3(x-1)   .........(1)

and y = 10x − 2x − 3 ......(2)

Simplify, both the equations,

y=5x + 3x - 3 = 8x - 3  

and y = 10x − 2x − 3 = 8x -3

Since, both equations are same.

So, the graph of both equation will overlap each other.

Hence,  the equation 5x + 3(x − 1) = 10x − 2x − 3 will have infinite many solution.

ANSWERED AT 21/02/2020 - 09:26 AM


QUESTION POSTED AT 21/02/2020 - 09:26 AM

If Circle A ~ Circle B, Circle A has a radius of 4, and Circle B has a radius of 2, what is the scale factor?

You would put circle A and circle B in a fraction form and then reduces it to simplest form so I am gonna put circle A on top then circle B on bottom 4/2 which reduces down to 2 circle A is 2 times bigger then circle B

ANSWERED AT 21/02/2020 - 09:16 AM


QUESTION POSTED AT 21/02/2020 - 09:16 AM

Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.

Did your explanation include the following?

Some polynomial equations have complex solutions.

Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.

Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.

ANSWERED AT 20/02/2020 - 11:21 PM


QUESTION POSTED AT 20/02/2020 - 11:21 PM

What are the x-intercepts of the quadratic function? y = x² + x – 2 1 2 and 1 2 and –1 –2 and 1

Your answer should be the last one, -2 and 1. Hope this helps!

ANSWERED AT 20/02/2020 - 11:20 PM


QUESTION POSTED AT 20/02/2020 - 11:20 PM

. What is the distance around a 2 Dimensional Shape?

The total distance around a closed shape (such as a rectangle) is known as the perimeter. 

ANSWERED AT 20/02/2020 - 11:20 PM


QUESTION POSTED AT 20/02/2020 - 11:20 PM

In 4 years, harry’s age will be the same as jim’s age is now. in 2 years, jim will be twice as old as harry will be. find their ages now.

The answer to this question would be:
Jim     =6 years
Harry =2 years

To answer this question, you need to translate the description into a  mathematical equation. If H= Harry's ages and J= Jim's ages, then the equation should be look like this:

1. H+4= J
2. (J+2)= 2(H+2)
     J+2= 2H+4
     J= 2H +2

If you put the 1st and 2nd equation together, the result would be:
H+4= J
H+4= (2H +2)
H-2H= 2-4
-H= -2
H=2

After that insert the H value to either 1st or 2nd equation.
H+4= J
2+4=J
J= 6

ANSWERED AT 20/02/2020 - 11:19 PM


QUESTION POSTED AT 20/02/2020 - 11:19 PM

If y = kx, what is the value of k if y = 20 and x = 0.4?

Set up an equation 20=k(0.4)....to find k divide 20 by 0.4

ANSWERED AT 20/02/2020 - 11:18 PM


QUESTION POSTED AT 20/02/2020 - 11:18 PM

If y = 3x -5 find the value of y when x = -1

Plug in negative 1 for x and do order of operations and u should get negative 8

ANSWERED AT 20/02/2020 - 11:18 PM


QUESTION POSTED AT 20/02/2020 - 11:18 PM

If x-y=8,find the value of y when x=3

3-y=8
-y=8-3
y=-5
so just try to re arrange the equation  to find the value for the variable

ANSWERED AT 20/02/2020 - 11:18 PM


QUESTION POSTED AT 20/02/2020 - 11:18 PM

If i take 2 cookies and had 2 more cookies, how many cookies do i have

4 an there is your answer

ANSWERED AT 20/02/2020 - 11:18 PM


QUESTION POSTED AT 20/02/2020 - 11:18 PM

If i run 10 kilometers in 1 hour how many kilometers do i run in 2 and a half hours

10 kilometers per hour
in 2.5 hours distance = 10 * 2.5 = 25 kilometers

ANSWERED AT 20/02/2020 - 11:18 PM


QUESTION POSTED AT 20/02/2020 - 11:18 PM

In the form f(x)=a(x-h)^2+k

Vertex is (h,k)
se see vertex is (1,-4)
y=a(x-1)^2-4
find a
another point is (4,-2)

-2=a(4-1)^2-4
-2=a(3)^2-4
-2=9a-4
add 4
2=9a
divide b 9
2/9=a


f(x)= \frac{2}{9}(x-1)^2-4

ANSWERED AT 20/02/2020 - 11:14 PM


QUESTION POSTED AT 20/02/2020 - 11:14 PM

Find the value of 2a 5b when a=-6 and b=2

2a = -12

5b = 10

Hope this helps
:)

ANSWERED AT 20/02/2020 - 11:14 PM


QUESTION POSTED AT 20/02/2020 - 11:14 PM

Evaluate 2.34 x 10 cubed

2.34 x 10 cubed
2.34 x 1000
2,340

ANSWERED AT 20/02/2020 - 11:13 PM


QUESTION POSTED AT 20/02/2020 - 11:13 PM

Corn cost 2$ for 6 ears . carmen bought 24 ears of corn. how much did she spend?

2/6=x/24
6x=48
x=8 dollars

ANSWERED AT 20/02/2020 - 11:12 PM


QUESTION POSTED AT 20/02/2020 - 11:12 PM

Charles has 24 marble. he has 6 more yellow marbles than blue marbles. what is the equation

Answer:

Required Equations are x + y = 24 & x - y = 6

Step-by-step explanation:

let x be the no of yellow marbles that Charles has.

and y be the no of blue marbles that Charles has.

Total Marbles that Charles has = 24

⇒ x + y = 24 ..............(1)

Charles has 6 more yellow marbles than blue marbles.

⇒ x = y + 6

    x - y = 6 ......................(2)

Therefore, Required Equations are x + y = 24 & x - y = 6

ANSWERED AT 20/02/2020 - 11:12 PM


QUESTION POSTED AT 20/02/2020 - 11:12 PM