Which coordinates best represents the vertex of the graph first correct answer gets Brianliest
Answers
Answer:
The vertex of the graph is:
the minimum point for a parabola that opens upwardsthe maximum point for a parabola that opens downwardsAs this parabola opens upwards, the vertex is the minimum point.
From inspection of the graph, vertex = (-3, -1)
Equation of the graph
From inspection we can see that the x-intercepts are when
x = -4 and x = -2
[tex]\sf x = -4 \implies x+4=0[/tex]
[tex]\sf x = -2 \implies x+2=0[/tex]
Therefore:
[tex]\sf y=(x+4)(x+2)[/tex]
Expand:
[tex]\sf \implies y=x^2+6x+8[/tex]
Answer:
[tex]B)f(x) = {x}^{2} + 6x + 8[/tex]
Step-by-step explanation:
Let [tex] f(x)=x^2[/tex] be the parent function. With transformation of function, firstly,we know that,
We can move it up or down by adding a constant to the y-valuealgebraically
g(x)=x²+CClearly, The parabola is moved down by 1 unit thus, C is -1. Therefore our function transforms to
f(x)=x²-1secondly, we know that,
We can move it left or right by adding a constant to the x-valuealgebraically,
g(x)=(x+C)²in case,
C is positive, g(x) moves to the left and vise versaSince the parabola is moved left by 3 unit, C is +3, and hence Our function eventually becomes
[tex]f(x) = (x + 3 {)}^{2} - 1[/tex]simplifying it yields:
[tex]\implies \boxed{f(x) = {x}^{2} + 6x + 8}[/tex]
Hence,B is our required answer
Related Questions
Find two solutions to the following system of inequalities. Please write it in ordered pair form.
Answers
Answer:
(5, 5) and (6, 1)
Step-by-step explanation:
Solutions to the system of inequalities are any points that are in the overlapped shaded region.
For example (5, 5) and (6, 1)
ProofFind the equations of the two lines.
Blue line
Two points on the line: (-5, 8) and (0, -7)
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-7-8}{0-(-5)}=-3[/tex]
Point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
[tex]\implies \sf y-(-7)=-3(x-0)[/tex]
[tex]\implies \sf y=-3x-7[/tex]
As the shading is above the line, and the line is dashed:
[tex]\sf y > -3x-7[/tex]
Red line
Two points on the line: (0, -9) and (2, 1)
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{1-(-9)}{2-0}=5[/tex]
Point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
[tex]\implies \sf y-(-9)=5(x-0)[/tex]
[tex]\implies \sf y=5x-9[/tex]
As the shading is below the line, and the line is solid:
[tex]\sf y\leq 5x-9[/tex]
[tex]\sf Inequality\:1: y > -3x-7[/tex]
[tex]\sf Inequality\:2:y\leq 5x-9[/tex]
Point (5, 5)
[tex]\sf Inequality\:1\implies -3(5)-7=-22 < 5\: \implies\:true[/tex]
[tex]\sf Inequality\:2\implies 5(5)-9=16 > 5\: \implies\:true[/tex]
Point (6, 1)
[tex]\sf Inequality\:1\implies -3(6)-7=-25 < 1\: \implies\:true[/tex]
[tex]\sf Inequality\:2\implies 5(6)-9=21 > 1\: \implies\:true[/tex]
the values in a data set r 15,7,11,12,6,3,10, and 6. where would u draw the box in a
Answers
Answer:
8.5
put numbers least to greatest and find the median by crossing numbers out front from back.
Pls help me with My math I need the ans rn, Tysm.
Answers
Answer:
35 degrees
30 degrees
PLEASE
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
y = -x - 4
Step-by-step explanation:
m = (-5-0)/(1+4) = -5/5 = -1
b = (0, -4)
y = mx + b
y = -x - 4
BRAINLIEST please if this helps!100 points and brainliest. Put nonesense and get reported. What is wrong with the equation below, make sure to explain
Answers
Answer: 1 3/4(8)= 14
Step-by-step explanation:
That is the correct answer
Solve the following problem.
360 mL =____cups?
type your answer...
Answers
Answer:
1.52 cups
Step-by-step explanation:
360 ml / (236.588 ml/cup ) = 1.52 cups
F(x)= x^2+2, g(x)= x+1, and h(x) =2x what is f(g(x)) when x= -1
Answers
= 0^2 + 2
= 2
Select the correct answer.
A regular octagon has side lengths of 8 centimeters. What is the approximate area
he octagon?
OA. 618 cm2
OB. 512 cm2
OC 309 cm2
OD
473 cm2
Reset
Next
Answers
Answer:
C. 309 cm2
Step-by-step explanation:
A=2(1+sqr2)a^2
A=2(1+sqr2)8^2
≈309.01934
Answer: 309 cm2
Step-by-step explanation:
plato
Giving brainliest! need this question rlly soon thank you so much :)
Answers
__________ is a time to challenge yourself and take some risks since your body is stronger than ever before, and you are changing and developing in all sorts of wonderful ways.
Answers
Answer:
Adolescence
Step-by-step explanation:
We are constantly changing and developing in adolescence, it is the bridge between childhood and adulthood, mixed with youth (taking risks more frequently, less worries) and responsibilities and coming-of-age.
Please, help me!!! 5 mins left to submit!!
Question 1 Part C (3 points): Choose the answer below that best completes the following statement:
Adding, subtracting, or multiplying two polynomials ___ results in another polynomial.
A. Sometimes
B. Always
C. Never
Answers
answer the following question
Answers
Answer:
Letters as in the attached image.
Triangles ABC and ADC are congruent by SSS. From that, corresponding angles are congruent, in parcicualre B and D, both measuring 94°.
Final angle is obtained by difference. The internal angles of a quadrilater add to 360, so the remaining is 360-90-94-94 =82°
Question 1 of 10
How many solutions are there to the equation below?
x² =-64
A. 0
B. 2
C. 16
D. 8
E. -8
Answers
To solve for x in this equation you must square root both sides, but since it is impossible to square root a negative number, there are 0 solutions.
Which of these statements is a valid perfect square trinomial?
Statement 1: x2 + 10x + 100 = (x − 10)2
Statement 2: a2 + 2ab + b2 = (a + b)2
Group of answer choices
Statement 1 and statement 2 are valid.
Statement 1 and statement 2 are invalid.
Only statement 1 is valid.
Only statement 2 is valid.
Answers
Answer:
D. Only statement 2 is validStep-by-step explanation:
Verify if the statements are correctStatement 1:
x² + 10x + 100 = (x − 10)²x² + 10x + 100 = x² + 2(x)(-10) + (-10)²x² + 10x + 100 = x² - 20x + 100LHS ≠ RHSStatement 2:
a² + 2ab + b² = (a + b)²a² + 2ab + b² = a² + 2ab + b²LHS = RSHAs we see the second statement is valid but not the first one.
Correct choice is D
Answer:
Statement 2 only
Step-by-step explanation:
2nd one is the identity so no need to verify its true
1st one
(x-10)²x²-20x+100Hence wrong
solve for x ~
[tex]4x - 16 = 64[/tex]
ty ^^
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \:4x - 16 = 64[/tex]
[tex]\qquad \sf \dashrightarrow \:4(x - 4) = 64[/tex]
[tex]\qquad \sf \dashrightarrow \:(x - 4) = 64 \div 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x - 4 = 16[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 16 + 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x =20[/tex]
[tex] \boxed{ \bf \huge \: Answer \: }[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x - 16 = 64[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x = 64 + 16[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x = 40[/tex]
[tex] \: [/tex]
[tex] \sf \large \: x = \cancel \frac{80}{4} [/tex]
[tex] \: \: [/tex]
[tex] \sf \large x = 20[/tex]
[tex] \: \: [/tex]
Hope It's Helps uh Miss<3"
If - 4x + 6y = 9 and -2x – 7y = -8 are true equations, what would be the value of -2x + 13y?
Answers
Answer:
17
Step-by-step explanation:
The expression of interest is the difference of the two given expressions.
(-4x +6y) -(-2x -7y) = (9) -(-8)
-2x +13y = 17
The value is 17.
_____
Additional comment
You could go to the trouble to solve the two equations for x and y, then compute the value of the expression you want. As we saw above, that is not necessary.
The first step in problem solving is always "look at the given information and how it relates to what you are asked." A little time spent doing that can save a lot of effort in the actual problem solving process.
What is the solution to the help!!!!!
following equation:
2(3x - 7) + 18 = 10
-
0 1
03
3
5
6
Answers
Answer:
x = 1
Step-by-step explanation:
Given:
2(3x - 7) + 18 = 10
Solution:
Subtract 18 from both sides
2(3x - 7) + 18 = 10
- 18 -18
---------------------------
2 (3x-7) = -8
Now divide both sides by 2
2 (3x-7) -8
----------- = ------------
2 2
Simplify
3x - 7 = -4
Then add 7 to both sides
3x - 7 = -4
+ 7 +7
--------------------
3x = 3
Divide both sides by 3
3x 3
----------- = ------------
3 3
x = 1
Thus, Solution : x =1
~Lenvy~
Answer:
[tex]x = 1[/tex]
Step-by-step explanation:
Step 1Simplify both sides of the equation
[tex]2(3x - 7) + 18 = 10[/tex]
Distribute
[tex](2)(3x) + (2)( - 7) + 18 = 10 \\ 6x + - 14 + 18 = 10[/tex]
Combine like terms
[tex](6x) + ( - 14 + 18) = 10[/tex]
[tex]6x + 4 = 10[/tex]
Step 2Subtract 4 from both sides
[tex]6x + 4 - 4 = 10 - 4[/tex]
[tex]6x = 6[/tex]
Step 3Divide both sides by 6
[tex] \frac{6x}{6} = \frac{6}{6} [/tex]
[tex]x = 1[/tex]
What value of x makes the equation true? 6 6x + 8 = 3x - 19 : A. X=-9 B. -- 3 C. = -3 D. x= 3
Answers
Answer:
A. x = -9
Step-by-step explanation:
6x + 8 = 3x - 19 <== subtract 3x from both sides
-3x -3x
3x + 8 = -19 <== subtract 8 from both sides
- 8 - 8
3x = -27 <== divide both sides by 3
/3 /3
x = -9
Hope this helps!
Answer:
[tex]\tt x=-9[/tex]
Step-by-step explanation:
[tex]\tt 6x + 8 = 3x - 19[/tex]
Subtract 8 from both sides:-
[tex]\tt 6x+8-8=3x-19-8[/tex]
[tex]\tt 6x=3x-27[/tex]
Subtract 3x from both sides:-
[tex]\tt 6x-3x=3x-27-3x[/tex]
[tex]\tt 3x=-27[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3x}{3}=\cfrac{-27}{3}[/tex]
[tex]\tt x=-9[/tex]
The vaule of x that makes the equation true is A) x= -9.
Three students measured the heights of the daffodils they are growing.
2/3
Sofia's daffodil is 4/6
of a foot high
Mateo's daffodil is
of a foot high.
3/8
Deshawn's daffodil is
of a foot high
Which statement correctly compares two of these fractions?
L
Answers
write in words
3a- 6
[tex] \frac{1}{2} z \: fy \: 10[/tex]
Answers
Answer:
See below ↓↓
Step-by-step explanation:
1) 3a - 6
6 minus the product of 3 and a2) 1/2zfy10
1/2 the product of z,f,y, and 10keith bought a soft drink for 2 dollars and 6 candy bars. he spent a total of 14 dollars. how much did each candy bar cost?
Answers
Answer:
2
Step-by-step explanation:
so if you take away 14 by 2 =12 and 12 divided by 6= 2
Answer:
each candy bar cost 2 dollars
Step-by-step explanation:
1. What is the cross section formed by cutting a cylinder perpendicular to its base?
2. What is the cross section formed by cutting a cone parallel to its base?
3. What is Cavalier's Principle? Can you think of an example applying it to everyday life?
…………….
Answers
Answer:
1
Depends on the cross section axis
place a cylinder can on a table , circular and side down .Look down at it and you see the other end so the cross section is circle
Turn it on its side and the cross section is rectangle
Suppose the Federal Reserve set the reserve requirement at 20%. Assume that banks lend all reserves that are not required to be held. Round the answers to two decimal places.
Answers
Answer:
whaaaat iisss these. answeeeeeeer??Help my sister please she needs help I don’t know because I forgot
Answers
Answer:
15 shrimps
Step-by-step explanation:
We already know that a small shrimp taco has 5 shrimps.
⇒ [tex]\text{1st equation: small shrimp taco = 5 shrimps}[/tex]
We also know that a large taco has 3 times more shrimps than a small taco.
⇒ [tex]\text{2nd equation: shrimps in a large taco = 3(Shrimps in a small taco)}[/tex]
Finding the number of shrimps in a large taco:
Now, simply substitute the number of shrimps in a small shrimp taco in the second equation to find the number of shrimps in a large taco.
⇒ [tex]\text{Shrimps in a large taco = 3(5) shrimps}[/tex]⇒ [tex]\boxed{\bold{\text{Shrimps in a large taco = 15 shrimps}}}[/tex]Answer:
15 shrimp
Step-by-step explanation:
5 shrimp * 3 = 15shrimp
Given the function f(x) = 4 - 2x, find f(3r - 1).
Answers
Answer:
6 - 6r
Step-by-step explanation:
we just plug in 3r - 1 instead of x
f(3r - 1) = 4 - 2(3r - 1)
= 4 - 6r + 2
= 6 - 6r
what is the total interest accured for a loan of $3200 at 6.1% interest
Answers
Answer:
6.1÷100×3200
press that you will get your answer
Susie has a rectangular dining room that has an area of 84. What is the area of the largest circular rug Susie can fit in her dining room?
Answers
Answer:
25[tex]\pi[/tex]
Step-by-step explanation:
[tex]\pi[/tex]r^2 is the formula for a circle (in this case, a circular rug)
and we would set it equal to 84 (since we are trying to get the biggest size possible).
We would isolate r so that r^2 = 84/[tex]\pi[/tex], and r would be around 5.17219.
If we were going by rounding 5 would be the largest radius possible and the radius would be 25[tex]\pi[/tex] or about 78.5398 units.
Answer:
Rounded to one decimal place, the maximum area circular rug that can fit in the dining room is 38.5 square feet.
Please See the attached screenshot for the exact solutions and answer for this question
A rectangular lot is 80 yards wide and 125 yards long.
Give the length and width of another rectangular lot that has the same perimeter but a smaller area.
Answers
Answer:
70 yards wide and 135 yards long
Step-by-step explanation:
The perimeter of a rectangle will be the same if the sum of length and width is the same. The area will be smaller if the difference between lenth and width is greater.
__
The sum of length and width will be the same if the length is increased by the same amount that the width is decreased. Changing each by 10 yards is one possibility.
A lot 70 yards wide and 135 yards long will have the same perimeter and a smaller area.
_____
Check
Given perimeter: 2(80 +125) = 410 yds.
Modified perimeter: 2(70 +135) = 410 yds. (same)
Given area = 80(125) = 10000 yd².
Modified area: 70(135) = 9450 yd². (smaller)
__
Additional comment
The area is greatest when the difference between the length and width is zero. That is, the rectangle will be a square.
Solve 96 =3w+ 15, where w is a real number.
2
Round your answer to the nearest hundredth?
Answers
Answer:
3+15=18 i guess
Step-by-step explanation:
dont judge me im only in 2 grade
What is the area of this trapezoid?
Enter your answer in the box.
__ ft²
Answers
Answer:
468 ft²
Step-by-step explanation:
Area = (37+15)/2 × 18
37 + 15 is 52
Divide 52 by 2 which is 26
26 × 18 is 468
We know,
[tex] \text{Area of trapezoid =} \frac{a + b}{2} h[/tex]
Here, a and b are base and h is height
Inserting The Values[tex] = \frac{37 + 15}{2} \times 18 \\ \\ = \frac{52}{2} \times 18 \\ \\ = \cancel\frac {52}{2} \times 18 \\ \\ = 26 \times 18 \\ = 468 \: \text{ft²}[/tex]
Hope This Helps