# 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

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.

## Related questions

### Mr. Wilson is giving his students a vocabulary test tomorrow over all the terms they have learned from this semester. Today, he wants to determine how prepared the students are for the test. So, he writes each term on a note card and puts all the note cards in a paper bag. Then, he asks each student to come to his desk, select five note cards out of the bag, define those five terms, and then put the note cards back in the bag. He records the number of terms each student is correctly able to define. What is the population in this situation? What is the sample? Use complete sentences in your answer. Do you think the data from the sample Mr. Wilson is collecting is representative of the population? Explain your reasoning using complete sentences.

The population in the above situation is the total number of students under Mr. Wilson.

A sample is a part of the population that may best represent the population. There is no sample  in the above situation because Mr. Wilson made all students pick 5 note cards. He will be able to determine the performance of each student based on their performance in picking 5 note cards and defining the terms in each card.

ANSWERED AT 21/02/2020 - 12:09 PM

QUESTION POSTED AT 21/02/2020 - 12:09 PM

### 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

### Two rectangles have the same width. The length of one is 2 feet longer than the width. The length of the other is 4 feet longer than the width. The larger rectangle has 8 more square feet than the smaller. What is the width of the rectangles?

Gtrrthsrtyu6hgrtysrthsthrthsrthgrty6

ANSWERED AT 21/02/2020 - 12:00 PM

QUESTION POSTED AT 21/02/2020 - 12:00 PM

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

Y=7x+2

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

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

### PLEASE HELP At Roberto’s construction site, the crew can frame a wall in 35 minutes and frame the opening for a door in 21 minutes. The crew needs 9 loads of materials for each wall and 13 loads of materials for each door. One day the crew worked for 595 minutes. and used 267 loads of materials. Which system of equations could be used to ﬁnd the number of doors. d. and walls. w, they framed? A 35w + 9w = 595 35d + 13d = 267 B 21w + 35d = 595 9w+ 13d= 267 C 35w + 21d = 595 13w+ 9d = 267 D 35w + 21d = 595 9w+ 13d= 267

ANSWERED AT 21/02/2020 - 11:16 AM

QUESTION POSTED AT 21/02/2020 - 11:16 AM

### What is the length of x

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

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

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

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

### Sorry, here's the real questions below. 70+ Points for Best 5 Answers! 1. A triangle has an area of 150 cm². What is the area of the triangle if the height of the triangle is reduced to of its original length? A. 25 cm² B. 75 cm² C. 50 cm² D. 10 cm² 2. A right rectangular prism has a volume of 96 cm³. What is the new volume of the prism if only the length of the prism is doubled? A. 588 cm³ B. 192 cm³ C. 96 cm³ D. 48 cm³ 3. The surface of a cube is 600 cm² What is the new surface area of the cube if the length of each edge of the cube is tripled? A. 5400 cm² B. 1800 cm² C. 200 cm² D. 900 cm² 4. What is the surface area to volume ratio of the rectangular prism? [SEE ATTACHMENT] A. B. C. D. 5. A rectangle has a perimeter of 30 cm. What would be the new perimeter if the length and width of the rectangle is doubled in size? A. 18 cm B. 60 cm C. 36 cm D. 120 cm

1) 75
2) 192 cm^3
3) 1800 cm^2
4) 19/20
5) 60 cm

ANSWERED AT 21/02/2020 - 09:17 AM

QUESTION POSTED AT 21/02/2020 - 09:17 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

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
2=9a
divide b 9
2/9=a 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 ### Paige and her family went to the movies. They bought 4 tickets and paid$12 for popcorn. They spent $40. How much did each ticket cost? Choose two answers: one for the equation that models this situation and one for the correct answer. A. Answer:$3 B. Answer: \$7 C. Equation: 12 + 4x = 40 D. Equation: 4 + 12x = 40

B. And C. Is the correct answer

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

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