Describe how the graph of y= x^2 can be transformed to the graph of the given equation.
y = x^2 - 12 (5 points)
a) Shift the graph of y = x2 left 12 units.
b) Shift the graph of y = x2 down 12 units.
c) Shift the graph of y = x2 right 12 units.
d) Shift the graph of y = x2 up 12 units.
Answers
Answer:
b
Step-by-step explanation:
Given y = x² then y = x² + c is a vertical translation of y = x²
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here c = - 12 < 0
Thus y = x² - 12 is the graph of y = x² shifted 12 units down → b
Answer:
b) Shift the graph of y = x2 down 12 units.
Step-by-step explanation:
Graphs
The graph of the function
[tex]y=x^2[/tex]
can be found by giving the variable x some values and calculating the values of y as follows:
For x=-2, [tex]y=(-2)^2=4[/tex]. Point (-2,4)
For x=-1, [tex]y=(-1)^2=1[/tex]. Point (-1,1)
For x=0, [tex]y=(0)^2=0[/tex]. Point (0,0)
For x=1, [tex]y=(1)^2=1[/tex]. Point (1,1)
For x=2, [tex]y=(2)^2=4[/tex]. Point (2,4)
The graph of
[tex]y=x^2-12[/tex]
Can be similarly found:
For x=-2, [tex]y=(-2)^2-12=-8[/tex]. Point (-2,-8)
For x=-1, [tex]y=(-1)^2-12=-11[/tex]. Point (-1,-11)
For x=0, [tex]y=(0)^2-12=-12[/tex]. Point (0,-12)
For x=1, [tex]y=(1)^2-12=-11[/tex]. Point (1,-11)
For x=2, [tex]y=(2)^2-12=-8[/tex]. Point (2,-8)
The graphs are shown in the attached image. It can be clearly seen that the second graph (in blue) is shifted down 12 units with respect to the red graph. Answer:
b) Shift the graph of y = x2 down 12 units.
Related Questions
72 = 5x + 22 X = can some one answer this plz
Answers
Answer:
x = 10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
72 = 5x + 22
Step 2: Solve for x
Subtract 22 on both sides: 50 = 5xDivide 5 on both sides: 10 = xRewrite: x = 10Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 72 = 5(10) + 22Multiply: 72 = 50 + 22Add: 72 = 72Here we see that 72 does indeed equal 72.
∴ x = 10 is the solution to the equation.
A parabola can be drawn given a focus of (4, -3) and a directrix of x=2 Write the equation of the parabola in any form
Answers
Answer:
The equation of the parabola ( y +3)² = 4 ( x-3)
Step-by-step explanation:
Step(i):-
we know that the focus of the parabola (h + a , k ) and directrix is x = h - a
Given
focus of the parabola (h + a , k ) = ( 4, -3 )
Equating h + a =4 ..(i)
and k =-3
Given directrix is x = 2
h - a =2 ..(ii)
Adding (i) and (ii) equations , we get
h + a + h-a = 4+2
2 h = 6
h =3
substitute h=3 in equation (i)
h + a =4
3 + a =4
a = 1
The length of Latus rectum 4a = 4(1) =4
Step(ii):-
The vertex ( h, k) = ( 3 , -3) and a = 1>0
Given directrix is x = h - a = 2 so the parabola axis is lie on X- axis and symmetric about x-axis
The equation of the parabola
( y - k )² = 4 a ( x - h )
( y - (-3))²= 4(1) ( x - 3 )
The equation of the parabola ( y +3)² = 4 ( x-3)
The regular price of a watch is $28.25. During a sale, the watch was marked 12% off. What was the price of the watch during the sale? (5 points)
a
$2.35
b
$3.39
c
$16.25
d
$24.86
Answers
Answer:
I believe the answer would be D, $24.86
Will mark brainliest
Answers
Please help with this question
Answers
Answer: Negative
Step-by-step explanation:
A is farther from 0 on the number line, whereas B is closer to zero. If A is negative and B is positive, B + A will be negative as the absolute value of A is greater than the absolute value of B (further from 0).
Answer:
The correct answer is B Negative
Step-by-step explanation:
When you are adding a negative, and a positive, if the negative will take over, and vice versa. For example if you were to add -8+3 it would equal -5.
Please help me! Thank you so much!
Answers
Answer: It's (A) 12<X
Step-by-step explanation: I chose that one because the line highlighted on the number line, it's bigger than 12!
Store A sells 5 bagels for $2.05. Store B sells 3 bagels for $1.35. How do the unit rates compare?
A. The bagels at Store A are $0.04 more expensive than the bagels at Store B.
B. The bagels at Store A are $0.03 more expensive than the bagels at Store B.
C. The bagels at Store B are $0.04 more expensive than the bagels at Store A.
D. The bagels at Store B are $0.03 more expensive than the bagels at Store A.
3 / 24
Answers
Answer:
C. The bagels at Store B are $0.04 more expensive than the bagels at Store A.
Step-by-step explanation:
Find the unit rates of both stores by dividing the price by the number of bagels:
Store A:
2.05/5
= 0.41
Store B:
1.35/3
= 0.45
Store B's bagels are $0.04 more than Store A's, so C is the correct answer.
the length of a rectangle is one unit more than its width. if the area of the rectangle is 56 square units,find the dimensions of the rectangle
Answers
Given:
The length of a rectangle is one unit more than its width.
Area of rectangle = 56 units
To find:
The dimensions of the rectangle.
Solution:
Let, width of the rectangle be x.
Then, length of the rectangle = x+1
Area of a rectangle is
[tex]Area=length\times width[/tex]
[tex]56=(x+1)\times x[/tex]
[tex]56=x^2+x[/tex]
[tex]0=x^2+x-56[/tex]
By splitting the middle term, we get
[tex]x^2+8x-7x-56=0[/tex]
[tex]x(x+8)-7(x+8)=0[/tex]
[tex](x-7)(x+8)=0[/tex]
Using zero product property, we get
[tex]x-7=0[/tex] and [tex]x+8=0[/tex]
[tex]x=7[/tex] and [tex]x=-8[/tex]
Width cannot be negative. So, x=7.
Now,
Width = 7 units
Length = 7+1
= 8 units
Therefore, the length of the rectangle is 8 units and width is 7 units.
Answer:
7
Step-by-step explanation: POV: I got it right
how to use standard form
Answers
Answer: Standard form is another way to write slope-intercept form (as opposed to y=mx+b). It is written as Ax+By=C. You can also change slope-intercept form to standard form like this: Y=-3/2x+3. Next, you isolate the y-intercept(in this case it is 3) like this: Add 3/2x to each side of the equation to get this: 3/2x+y=3.
Step-by-step explanation: hope this helps
One afternoon, 27 people withdraw $100 from an ATM. What was the overall change in the amount of money in the machine?
Answers
Answer:
The change is a decrease of $2700.
Step-by-step explanation:
Given
Total Number of people = 27
Amount each person withdrew = $100
The total withdrawn amount by 27 people = 100 × 27
= $2700
Let M be the amount of money in the ATM at the beginning.
As $2700 was drawn from the ATM, therefore, the change the amount of money in the machine will be:
M - 2700It means the change is a decrease of $2700.
Suppose you know that the volume of the following prism is represent by V(x) = -2x^3 + 14x^2 + 120x.
Answers
Step-by-step explanation:
-2x³ + 14x² + 120x
= -2x(x² - 7x - 60)
= -2x(x - 12)(x + 5).
The other 2 dimensions are -2x and (x + 5).
When using a graphing calculator to maximise the volume of the prism, we get x = 7.378. However this value is not reasonable as it makes -2x and (x - 12) negative, which are the sides of the prism.
Lily says that (2+i)" is a complex number for every positive integer value of n. Explain how you
know Lily is correct.
Answers
Melissa had $20 to purchase candy for a party. She purchased 3.6 pounds of candy that cost $2.50 per pound. How much money does Melissa have remaining after this purchase?
Answers
Answer:
1738
Step-by-step explanation:
Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Melissa had $20 to purchase candy for a party.
She purchased 3.6 pounds of candy that cost $2.50 per pound
Melissa spent 3.6 x $2.50
= 9 on candy.
Subtracting this amount from her initial $20, we get:
$20 - $9 = $11
Therefore, Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
What is the distance between point A and B , to the nearest tenth ?
Answers
Mr. Kaffey used a full 3-liter bottle of soda to fill two containers. He put 0.276 liter of soda in the first container. He put 0.92
liter of soda in the second container. How many liters of soda remained in the bottle?
Answers
Answer:
1.804 L
Step-by-step explanation:
The highest point in a park is 235 feet above sea level. The lowest point is 32 feet below sea level. What is the distance between the highest and lowest points in the park? _____ feet
Answers
Answer:
The distance between the points is equal to 267 feet
Step-by-step explanation:
In order to find the distance between the highest and the lowest points in the park we just have to subtract the the lower height from the higher height and the resulting difference will be equal to the distance between the two points. And so we get..........
235 - (-32) = 235 + 32 = 267
(Notice that the 32 feet are written as (-32) because the lowest point is 32 feet below the sea level).
add above sea level and below sea level
use a calculator and work out the following and write all the figures from your work display. a) (6.2 - 3.51) x (11.7 x 0.3)
Answers
Answer:
Solving the expression: [tex](6.2 - 3.51) \times (11.7 \times 0.3)[/tex] we get 9.4419
Step-by-step explanation:
We need to solve the expression: [tex](6.2 - 3.51) \times (11.7 \times 0.3)[/tex]
According to DMAS rules first we solve brackets and then we will multiply the results found after solving brackets
So,
[tex](6.2 - 3.51) \times (11.7 \times 0.3)\\=2.69 \times 3.51\\=9.4419[/tex]
First we solved the terms (6.2-3.51) and get 2.69 and by solving (11.7 x 0.3) we get 3.51
Now, we will multiply 2.69 with 3.51 to get the final result.
The final result is 9.4419
So, solving the expression: [tex](6.2 - 3.51) \times (11.7 \times 0.3)[/tex] we get 9.4419
PLEASE HELP ME I DONT KNOW HOW TO ANSWER THIS
Answers
Answer:
I think its SAS but it i took geometry 2 years ago so im not 100% sure
Step-by-step explanation:
pls help meeeeeeeeee
Answers
Question 2- 1.< 2.< 3.>= 4.< 5.>= 6.>
Bob and Cheryl are taking a road trip that is 181.60 miles. Bob drove
3
4
of the total distance.
How many miles did Bob drive?
Answers
A recipe calls for 4 0z of raisins. If I
use 224 0z of raisins, how many
batches of this recipe did I make?
Answers
Ms. Sanger blended 8 ¾ gallons of iced tea with some lemonade for a picnic. If there were 13 ⅖ gallons of the beverage, how many gallons of lemonade did she use?
Answers
13 2/5- 8 3/4= 4.65 or 4 13/20
Hope this helps you!
Dan earns £367 over the course of a five day week. How much is that per day?
Answers
One day = 367/5
Answer: £73.40
Would a graph with a slope of 0 and a y intercept of 4 be proportional or not proportional?
Answers
9514 1404 393
Answer:
not proportional
Step-by-step explanation:
If the y-intercept is not zero, the graph does NOT show a proportional relationship. A y-intercept of 4 means the relation is not proportional.
What is the slope of the line represented by the equation 3x+4y= 12?
A: - 4/3
B: - 3/4
C: 3/4
D: 4/3
Answers
Answer:
B: -3/4
Step-by-step explanation:
1/x+2=2/x-1 identify all values of X that make the equation true
Answers
9514 1404 393
Answer:
as written: x = 1/3
as maybe intended: x = -5
Step-by-step explanation:
As written
(1/x) +2 = (2/x) -1
3 = 1/x . . . . . . . . . add 1-(1/x)
x = 1/3
__
As maybe intended
1/(x +2) = 2/(x -1)
x -1 = 2(x +2) . . . . . . . multiply by (x+2)(x-1)
x -1 = 2x +4 . . . . . . . . eliminate parentheses
-5 = x . . . . . . . . . . . . . subtract (x+4)
CAN I HAVE SOME HELP!!!!
Answers
Answer:
I believe is C
if not I'm sorry.
You split 5 1/2 hours of volunteer equally over the next three weeks. How much time will you volunteer each week? Label your answer. Place your answer in simplest form. Convert any improper fractions to mixed numbers.
Answers
Answer:
answer my question
Step-by-step explanation:
Tell whether the sequence is arithmetic. If it is, identify the common difference. 4, 8, 16, 32, …
Answers
Answer:
it's geometric
8/4=2 16/8=2
d=2
HELP ME ALSO SHOW WORK PLEASE #3
Answers
Answer:
(3,-7)
Step-by-step explanation:
i’ll explain in the comments :)