Graph the equation y = x2 + 8x + 12 on the accompanying set of axes. You must
plot 5 points including the roots and the vertex. Using the graph, determine the
vertex of the parabola.
Answers
Answer:
Step-by-step explanation:
Roots: set y = x^2 + 8x + 12 = 0 and solve for x: x + 6 = 0, so x = -6 is one root. The other is x = -2. The corresponding points are (-6, 0) and (-2, 0).
y-intercept: Let x = 0. Then y = 12. The y-intercept is (0, 12).
Axis of symmetry: x = -b / (2a) => x = -8/(2*1) = -4: x = -4
Vertex y-value: evaluate y at x = - 4: (-4)^2 + 8(-4) + 12 = -4: (-4, -4)
Arbitrarily chosen x value: x = 1 => 1^2 + 8(1) + 12 = 21: (1, 21)
The five points are: (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21). The vertex is (-4, -4). The parabolic graph opens UP.
The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² + 8x + 12
Conver the equation into a vertex form. Then we have
y = x² + 8x + 12
y = x² + 8x + 16 - 16 + 12
y = (x + 4)² - 4
The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).
The graph is given below.
More about the equation of the parabola link is given below.
https://brainly.com/question/20333425
#SPJ2
Related Questions
LOOK AT PROVIDED IMAGES PLZ! Problem worth a lot of points if right!!
Answers
Answer:
add and subtract
Isabel received a $90 gift card for a coffee store she used it in buying some coffee that cost $7.46 per pound after buying the coffee she had $67.62 left on her card how many pounds of coffee did she buy
Answers
Answer:
3 pounds
Step-by-step explanation:
Amount spent
90 - 67.62 = 22.38
coffee bought
22.38/7.46 = 3 pounds
Doug is going to ride his bicycle 3,000 miles across the United States, from coast to coast. He wants to choose the route that will give him the greatest chance of success. Here's what he finds in his research:
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Answer: hello your question has some missing data below is the missing data
There have been 2 attempts on the northern route from Maine to Washington. Both of those riders made it 2,000 miles and quit in Montana. There have been 19 attempts on the central route from Virginia to California; 9 of those riders didn't make it out of Virginia and the other 10 made it all the way to the Pacific. There have been 32 attempts on the southern route from Florida to San Diego. One of those riders made it the whole way. Another realized he was out of shape, and quit before he even started. The other 30 riders quit somewhere in Texas. They were evenly distributed between 1 , 300 and 1 , 700 miles. For the northern route, the median distance covered will be the mean. For the central route, the median distance covered will be the mean. For the southern route, the median distance covered will likely be the mean
answer : Doug should choose the Central route
Step-by-step explanation:
Number of Available routes = 3
Northern route ; Total distance covered = 2000 miles
Central route : Total distance between Virginia and California = 2818.5 miles
percentage of success = 10 / 19 * 100 = 52.63 %
Mean distance covered = 2818.5 * 52.63% = 1483.38 miles
southern route
Distance to be covered = 2,548 miles
number of attempts = 32
percentage of success = 1 = ( 1 / 32) * 100 = 3.12%
median distance covered by 30 riders = 1300 + ( 400 / 30 ) = 1313.33
Conclusion :
Doug should choose central route because it has the highest percentage of success and longest distance covered ( i.e. closest to 3000 miles ) and it is also coast to coast
Austin’s monthly gross pay is $4,200. Federal withholding is 16.05% of his pay. His other deductions total $321.30. What is his net pay.
Answers
Answer:
$3,204.6
Step-by-step explanation:
$ 4,200 represents 100% of his salary
x amount of $ represents 16.05 % in federal withholding
after you line up $ with $ and % with % think cross multiplication
x = 4,200* 16.05/ 100 = $674.1 is the amount in federal withholding
Net pay = 4,200 -674.1 -321.30 = $3,204.6
A sheet of cardboard 12 inches square is used to make an open box by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with the largest possible volume
Answers
Answer:
[tex]x=6+3\sqrt{2}[/tex] is the size of the square
Step-by-step explanation:
Let the side of the square cut from the cardboard be “x”
Size of the square base = [tex]12 -2x[/tex], height of the box = x
Volume of square box = Area * height = [tex](12-2x)^2 * x[/tex]
Differentiating the above equation and equating it to zero, we get –
d/dx [tex]((12-2x)^2 * x)[/tex]
d/dx[tex]{(144 + 4x^2 -48x)*x}[/tex]= d/dx [tex](144x + 4x^3 -48x^2)[/tex]
d/dx [tex](144x + 4x^3 -48x^2) = 0[/tex]
[tex]144+8x^2-96X= 0\\18 +X^2-12X = 0[/tex]
On solving above equation, we get –
[tex]x=6+3\sqrt{2} \\ x=6-3\sqrt{2}[/tex]
Rahul has 5 BLUE BLOCKS, 3 PINK BLOCKS AND 4 GREEN BLOCKS. He wants to count the total number of blocks he is having. In how many ways he can find the answer? Form a mathematical expression to find the total number of blocks and identify the property used.
Answers
Answer:
a) He can find the answer in one way
b) We make use of Addition property of mathematics
c) Total number of blocks = 12 blocks
Step-by-step explanation:
a) He can find the answer in one way
b) We make used of addition property of mathematics
c) The total number of blocks he is having is calculated as:
Blue blocks + Pink blocks + Green blocks
Where
Blue blocks = 5
Pink blocks = 3
Green blocks = 4
Hence:
Total number of blocks = 5 + 3 + 4 = 12 block
Which of the following diagrams shows the numbers in the correct sets?
Answers
Now this problem
HELP HELP HELP FIRST RIGHT ANSWER GETS BRAINLIEST
Answers
Answer:
No solution
Step-by-step explanation:
2x - y = 8
2x - y = 6
They are the same unknown variable, if they equate different things, there is a problem.
bcs 2x-y - (2x - y) = 2x - 2x - y + y = 0
but 8-6 ≠ 0
Thus this is unsolvable.
expand 5(8x - 3y) to its simplest form
Answers
Answer:
40x - 15y
Step-by-step explanation:
Multiply the brackets together
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Have a good day :)
Answer:
40x - 15y
Step-by-step explanation:
Use the distributive property:
5(8x) - 5(3y) =
40x - 15y
Solve for x. Round your answer to the nearest tenth
Answers
answer
tan x=p/b=8/15
Step-by-step explanation:
using pythagoras theorem
h^2 =p^2+b^2
h^2=8^2+15^2
h^2=64+225
h^2=289
h=root 289
h=17
then,
cosx=b/h
=15/17
^2= Square
Please helppp it would be much appreciated
Answers
Answer: B is the correct answer!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Well since you pretty much know that electrons are negative soo... B
Find all possible values for each expression.
tan-1 1
Answers
Answer:
45 and 225degrees
Step-by-step explanation:
Given the expression
tan⁻¹1
Using the calculator
tan⁻¹1
tan⁻¹1 = 45degrees
Since tan is positive in the third quadrant
theta= 180 + theta
theta = 180 + 45
theta = 225degrees
Hence the values of theta are 45 and 225degrees
32 + (-32) is an example of:
proportion
additive Inverse
absolute value
ratio
Answers
Answer:
Addituve Inverse
Step-by-step explanation:
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
Answer:
additive Inverse or absolute value
Step-by-step explanation:
EASY MATH PLEASE HELP! :)
I WILL GIVE BRAINLIEST!
QUESTION: Find the area!
Answers
Answer:
256ft
Step-by-step explanation:
18 times 8 plus 16 times 16 divided by 2
hope this helps! :D
So,
Area of ta rectangular,
=Length*width
16*8
128ft squad
Next one is,
Area of triangular,
Formula of area of triangular,
1/2*Feet*Hight
1/2*16*8
64
So
Want to addition 2 Answers,
128+64
192ft squad
A t-shirt is launched into the stands at a game. The equation h(x) = -16x2 + 48x + 6 models the relationship between time x and the height of the t-shirt h(x). List the calculation you must complete to find the answer to each question.
1. How high off the ground is the t-shirt launcher?
2. How high is the t-shirt after 1 second?
3. When does the t-shirt reach its maximum height?
4. What is the maximum height of the t-shirt?
5. When will the t-shirt reach the ground again if nobody catches it?
Answers
Answer:
1) 6 feet
2) 38 feet
3) at 1.5 seconds
4) 42 feet
5) in 3.12 seconds
Step-by-step explanation:
Please help
No links as they don’t work
Will mark brainliest
Answers
Pls someone help I need help with 2 I need answer and explanation pls
Answers
Answer:
2. B, 18 = 11 + 7
If you plug in the 7 in the y it would make sense
18 = 11 + y
Let's plug in the 7
18 = 11 + 7
and 11 + 7 = 18, so it makes sense! Therefore B is your answer for question number 2.
Answer:
B. 18 = 11 + y
Step-by-step explanation:
since y = 7
substitute it into the equation which becomes
18 = 11 + 7
which makes this statement true.
11 + 7 = 18
Please follow me
Type: "Follow KelvinSu From:(your name)"
Thank you in advance
Answers
Follow KelvinSu From: Thadd
The sum of two numbers is 75. The second number is 3
less than twice the first. Find the numbers. Please give me the answer step by step on how to solve it.
Answers
x + (2x-3) = 75
now add both together
3x-3 =75
move over the constant
3x=78
and divide by 3
x= 26
Hope this helps!!
Answer:
x= 26 y = 49
Step-by-step explanation:
let the first number be x and second be y
then
according to the question,
x + y= 75
x + (2x- 3) = 75
x + 2x - 3 = 75
3x = 75 +3
3x = 78
x = 78/3
x = 26
thus first number is 26
and second number is 2x-3=2×26-3
= 52 - 3= 49
if x/ 3=3/x then what is the value of x
1.-3
2.3
3.+-3
Answers
Answer:
x = ±3 (Option 3)
Step-by-step explanation:
[tex]\frac{x}{3} = \frac{3}{x}[/tex]
Multiply both the sides with 3.[tex]=> \frac{x}{3} \times 3 = \frac{3}{x} \times 3[/tex]
[tex]=> x = \frac{9}{x}[/tex]
Multiply both the sides with 'x'.[tex]=> x \times x = \frac{9}{x} \times x[/tex]
[tex]=> x^2 = 9[/tex]
Root-square both the sides.[tex]=> \sqrt{x^2} = \sqrt{9}[/tex]
[tex]=> x = (+3) \: or \: (-3)[/tex]
∴ x = ±3
Taxi A charges $0.25 per mile and an initial fee of $5. Taxi B charges $0.5 per mile and an initial fee of $2. In how many miles will the cost of Taxi B will be the same than Taxi A.
Answers
Answer:
12 miles
Step-by-step explanation:
Let
x = number of miles
Taxi A:
5 + 0.25x
Taxi B:
2 + 0.5x
In how many miles will the cost of Taxi B will be the same than Taxi A
Equate cost of taxi A and taxi B
5 + 0.25x = 2 + 0.5x
Collect like terms
5 - 2 = 0.5x - 0.25x
3 = 0.25x
Divide both sides by 0.25
3 / 0.25 = 0.25x / 0.25
x = 3/0.25
x = 12 miles
x = number of miles = 12 miles
Which of the following rational numbers lies between 1/3 and 2/3?
Answers
24/48, 20/48, 18/48, 17/48
==========================================================
Explanation:
1/3 = 0.333 approximately
2/3 = 0.667 approximately
We're looking for values between 0.333 and 0.667
We can rule out choice A because 1 doesn't fit the description.
Choice C can be ruled out as well because 9/12 = 0.750 isn't between 0.333 and 0.667
--------------------------
Choice B works because all the decimals shown below are between 0.333 and 0.667
24/48 = 0.50020/48 = 0.417 (approximate)18/48 = 0.37517/48 = 0.354 (approximate)find the range of these sets of data -2,9,-1,-2000,-6000
Answers
Step-by-step explanation:
the given data is in ascending order=9,-1,-2,-2000,-6000
rang = 9-(-6000)
( from above photo it continue )
what is the value of r if 3r =243?
Answers
Answer:
243 divided by 3 equals 81 so r=81
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
Simplify the equation. 3r=243, so divide 3 on both sides, and you get r=81, hence 81 is the answer.
I'm quite confused on which answer is it Please help.
Answers
Answer:
[tex] \rm Option \; D [/tex]
Step-by-step explanation:
→ Volume of cube = (l)³ cubic units
l denotes length of the side→ Volume of cube = 1 unit × 1 unit × 1 unit
→ Volume of cube = 1 cubic unit
Option D is correct. ☑
Math screen shot photo
Answers
Answer:
30625
Step-by-step explanation:
Answer:
175²
Step-by-step explanation:
7 × 7 × 5 × 5 × 5 × 5
= (7 × 7) × (5 × 5 × 5 × 5)
= 7² × 5⁴
= 49 × 625
= 30.625
[tex] \sf = \sqrt{30.625} [/tex]
[tex] \sf = \sqrt{175 \times 175} [/tex]
[tex] \sf = 175[/tex]
[tex] \sf = {175}^{2} [/tex]
Conclusion:
Exponential Form of 7 × 7 × 5 × 5 × 5 × 5 adalah 175².
Solve(100 points to right answer)If you get it wrong or type random stuff you will be reported
Answers
Answer:
24 ft
Step-by-step explanation:
Hypotenuse = √9²+16²=√81+256=√400=20ft
the upper side of the stuff = 4 ft
total = 20+4=24
i hate copy and pastes
Answers
Answer:
why they're so helpful
Step-by-step explanation:
Answer:
Me too it so much wooooorrrrkkk
Step-by-step explanation:
"The ratio of five less than thrice a number x and four" please write in symbols
Answers
Answer:
(3x - 5)/4
Step-by-step explanation:
(3x - 5)/4 desribes five less than thrice a number x over four. Please let me know if this is what you mean.
Please help!!! Giving brainliest and extra points!!!! (Click on the photo)
Answers
Answer:
2400 inches cubed
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
V=whl
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So the formula is telling us to multiply the width, height, and length together. So in that case:
10 × 12 × 20 = 2400
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Have a good day :)