Answers
9514 1404 393
Answer:
a) y = (x -4)² -4
b) (4, -4)
c) translated 4 right, 4 down
Step-by-step explanation:
a) Apparently "graphing form" is a reference to "vertex form." That form is ...
y = a(x -h)² +k . . . . . . parabola with vertex (h, k) and vertical scale factor 'a'
The coefficient of x² in your given equation is 1, so a=1. The values of h and k can be found as follows.
'h' is the opposite of half the x-coefficient in your equation, so is h = -(-8/2) = 4. The value of k is the square of h, subtracted from the constant in your equation: k = 12 -h² = 12 -16 = -4. (This applies when a=1, as here.) These calculations are the "cut to the chase" version of "completing the square."
The method of "completing the square" has you consider the x-terms separately from the constant term:
y = (x² -8x) +12
To "complete the square", you want to make the terms in parentheses be a perfect square trinomial. You do that by adding the square of half the x-coefficient. In order to keep the same equation, you need to subtract an equivalent amount outside parentheses:
y = (x² -8x +(-8/2)²) +12 -(-8/2)² . . . . . add and subtract (-8/2)²
y = (x -4)² +(12 -16)
Then the vertex form is ...
y = (x -4)² -4 . . . . and the vertex is (h, k) = (4, -4).
The graphing calculator plot attached confirms this vertex value.
__
The problem statement tells you that you can also find this form by averaging the x-intercepts. If you factor your equation, you get ...
y = (x -6)(x -2)
The x-values that make these factors zero {6, 2} are the x-intercepts. Their average (6+2)/2 = 4 is the x-coordinate of the vertex (h). You can find the y-coordinate of the vertex by evaluating y when x=4: y = 4² -8·4 +12 = -4. So, the vertex by this method is (h, k) = (4, -4), and the equation in graphing form is ...
y = (x -4)² -4 . . . . as above.
__
b) As we saw above, the vertex coordinates are (h, k) = (4, -4).
__
c) The vertical scale factor 'a' is 1, so the only transformation done on the graph is to move the parent vertex (0, 0) to the location (4, -4). That is, the graph has been translated 4 units right and 4 units down. (In the attached, the parent function is shown with a dashed line.)
Related Questions
Carrie Crop Growers square garden has a side length of 12 feet. What is the area of the garden? What is the perimeter?
Answers
Answer:
Area = 144 Perimeter = 48
Step-by-step explanation:
if the garden is square and the length is 12 all you do is 12 * 12 for the area and 12+12+12+12 for the perimeter.
Jayden and Jacques went to the park to play. They were gone for an hour and fifteen minutes. They ot home at 12: 30 pm. What time did they leave for the park?
Answers
Answer:
11 : 15 am
Step-by-step explanation:
one hour before 12:30 pm is 11:30 am
15 minutes before 11:30 am is 11:15 am
Answer:
11:15
Step-by-step explanation:
To solve this question we basically have to subtract 1 hour and 15 minutes from 12:30.
1230
- 0115
-------------
11:15 a.m.
So the answer would be they left for the park at 11:15 a.m.
In conclusion, Jayden and Jacques left for the park at 11.15 a.m.
plz give me brainliest :)
In the figure, angle E measures 54° and angle G measures 29°. What is the measurement of angle H?
A.
25°
B.
34°
C.
97°
D.
126°
Answers
Answer:
H=97 degrees or choice "C"
Step-by-step explanation:
Assuming this is a triangle:
All triangles contain 180 degrees, so:
180=E+G+H, or H=180-E-G
H=180-54-29
H=97
H=97 degrees or choice "C"
Which is the solution to the system of equation? (3x + y= 11 y= x + 3)
Answers
Answer:
(2,5)
Step-by-step explanation:
The intersection point of 3x+y=11 and y=x+3 is (2,5) on a graph.
for what value of x is d parallel to e?
A) 20
B) 25
C) 35
D) 37
Answers
9x = 180
X= 20
A is the answer
Hope this helps! Have a great day ^W*
A square has a perimeter of 8x - 10 units, Each side is x units long. What is the value of x?
Answers
Answer:
They want you to recognize that you can make 2 equations that both are equal to P.... the perimeter.... and then set them equal to each other and solve for x .. as below
Step-by-step explanation:
P = 8x-10
P = 4x
4x = 8x-10
10 = 4x
2.5 = x
LIS
Find the minimum value of
C = 6x + 7y
Answers
Answer:
x= c−7y/6
Step-by-step explanation:
A rational numbers are ______ Integers
Answers
Answer:
A rational number is a fraction of 2 integers.
Tyler has a baseball bat that weighs 28 ounces. Find this weight in kilograms and in grams. Explain or show your reasoning. (Note: 1 kilogram 35 ounces)
Answers
Answer:
Weight in Kilograms = 0.8 Kilograms
Weight in grams = 800 grams
Step-by-step explanation:
Tyler has a baseball bat that weighs 28 ounces.
a) Weight in Kilograms
From the question:
1 kilogram = 35 ounces
Hence:
35 ounces = 1 kilogram
28 ounces = x kilogram
Cross Multiply
35 × x = 28 × 1
x = 28/35
x = 0.8 kilograms
b) Weight in grams
1 kilogram = 1000 grams
0.8 kilogram = x
Cross Multiply
x = 0.8 × 1000 grams
x = 800 grams
What is the sum of the two expressions?
(2/5x + 3) + (1/5x − 1)
Answers
Answer:2+ 3/5x
Step-by-step explanation:
Chad has a bag with 2 mint sticks, 11 jelly treats, and 7 fruit tart chews. If he eats one piece every 4 minutes, what is the probability his first two pieces will be a jelly treat and a mint stick and represent as a percent to the nearest tenth if necessary?
Answers
Answer:
first you add all the candies together to get 20 in the bag
2+11+7=20
jelly treat:
now we divide 11 by 20 to get a decimal
11/20= .55
multiply .55 by 100 to change it to a percentage
.55*100=55
first part of answer: He has a 55% chance of getting a jelly treat
mint stick:
divide 2 by 20 to get a decimal
2/20=.1
change .1 to a percent by multiplying by 100
.1*100=10
second part of answer: he has a 10% chance of getting a mint stick
Step-by-step explanation:
Find WZY. (helpp fast)
Answers
Answer:
[tex]m\angle WZY = 24^\circ[/tex]
Step-by-step explanation:
Angles and Lines
The figure shows two triangles WXZ and WYZ. Considering:
* Angles WXZ and WYZ are right (90°)
* Sides XW and YW are congruent (red marker on both)
* They share the side WZ.
We can conclude they are congruent. Thus, angles XZW and YZW are congruent or have the same measure:
5x + 4 = 6x
Subtracting 5x:
4 = x
Or, x =4
Thus:
[tex]m\angle WZY = 6x = 24^\circ[/tex]
[tex]\mathbf{m\angle WZY = 24^\circ}[/tex]
what is the power to 2
Answers
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
QUICK HELP ME PLEASEEEEEEE. ONLY ONE HOUR LEFT! WILL MARK BRAIN...
Answers
Answer:
copy and paste it to math website
Step-by-step explanation:
If you are good at data and graphs, pls help me! Use the screenshot below!
Answers
Answer:
400
Step-by-step explanation:
What is the approximate area of the circle shown below? Please help and thank you
A. 11.6 ft2
B. 172 ft2
C. 23.2 ft2
D. 43 ft2
Answers
Answer:
D
Step-by-step explanation:
A = (pi)(r)^2
A = (3.14)(3.7)^2
A= ~43
Answer:
d. 43
Step-by-step explanation:
HELP ME PLEASE!!!!!!!!!!!!!!!! You have to figure out whether its undefined or zero
Answers
Answer:
It's an undefined slope
PLEASE ANSWER
What is a ratio?
Answers
The quantitative and relatable relation between two amounts of goods or numbers shows the number of times one value contains or is contained within the other or one number/value with respect to the other number/value.
It is basically the relationship between two similar magnitudes with respect to the number of times the first contains the second.
Lets us understand this with the help of an example that the ratio of x to y can be written as
x: y x / yExample: the ratio of 1 to 2, written 1:2 or 1/2.
Know more about Ratio: https://brainly.com/question/12024093
6's + 2) = 18
S+2=
S=
Answers
Answer:
s+2=3
s=1
Step-by-step explanation:
make it braintliest please
2.1834 around you to the nearest hundredth
Answers
Answer:
2.18 I think this is the answer sorry if it's not-
Answer:
2,1044 is the correct answere
Dale buys candy that costs $8 per pound. He will buy at least 7 pounds of candy. What are the possible amounts he will spend
on candy?
Use c for the amount (in dollars) Dale will spend on candy,
Write your answer as an inequality solved for c.
Answers
Answer:
66
Step-by-step explanation:
Plz help me i need it BRAINLIEST AND GOOD RATING IMMEDIATLY
Marcus and Lily are running at the school track. The graphs below represent the distance in miles each person has run as function of time in minutes. Select all the statements that are true based on the graphs shown.
Answers
Select the reason why these triangles are
similar. If they are not, select "Not similar".
A. AA
B. SAS
C. SSS
D. Not similar
Answers
Answer:
B. SAS
Step-by-step explanation:
In the given diagram, it would be observed that each side of the bigger triangle are multiplied by a factor of [tex]\frac{1}{3}[/tex] to give the values of each corresponding sides of the smaller triangle. But the included angle of the two triangles are the same.
Therefore, the reason why the triangles are similar is because of side-angle-side (SAS) relations. The correct option is B.
Answer:
SAS
Step-by-step explanation:
Just Because.
I really need help solving this equation plss!! 40 points
Answers
Answer:
a1 (-5, -3)
b1 (-1, -2)
c1 (2, -3)
d1 (-4, -5)
Step-by-step explanation:
Everything lowers by 6 squares
You go to the mall and your mom gives you $60 to spend on back to school clothes. There is a shirt you want for $80, but it is 25% off. Will you have enough money?
Answers
Answer:
yes you will
Step-by-step explanation:
25% off of 80 is 60
Activity 12.1 Tax, Tip, and Discount
What percentage of the car price is the tax?
car price
tax
Answers
Answer:
25%
Step-by-step explanation:
(1/4)x100=0.25x100=25, The tax is 25%
Find the exact length of the third side.
39
36
Answers
The answer is 15 cm
39 cm, 15 cm, 36 cm
Pls pls help I don’t have time HELP ASAP. It also detects if it’s right or wrong.
Answers
Answer:
360
Step-by-step explanation:
hope this helps.
Below are two parallel lines with a third line intersecting them.
Answers
Answer:
132 degrees
Step-by-step explanation:
One sit of the 48 degrees is 48 degrees, so that opposite will be the same. Add them up, get 96. There is a full 360 degrees circle, so get 360 and subtract 96 from it, to get 264 degrees. That is the top and bottom angle of the right side, so just divide it in two
Answer:
I think x= 84
if the lines are parallel then the angle should be the same. Because one angle =48° the other side is likely to equal the same. Add 48+48, subtract 180 from your answer and that's how you get 84°. hope this helps
Find the length of the third side to the nearest tenth. a=4 b=6 c=?
Answers
Answer:
[tex]2\sqrt{13}[/tex]
Step-by-step explanation:
