Answers
We can use the quadratic function in vertex form, f(x) = a(x - h)^2 + k where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the parent function wider or narrower.
* If a is positive, the graph opens up.
* If a is negative, the graph opens down.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Now that we defined each variable in the vertex form, we can plug in the values of the vertex (-4, 3) into the equation:
f(x) = a(x - h)^2 + k
f(x) = a(x + 4)^2 + 3
To solve for the value of “a”, we must choose another point from the graph. The y-intercept of the parabola happens to be (0, 19), so we’ll use its values to solve for “a”:
19 = a(0 + 4)^2 + 3
19 = a(4)^2 + 3
19 = a(16) + 3
Subtract 3 from both sides:
19 - 3 = a(16) + 3- 3
16 = 16a
Divide both sides by 16:
16/16 = 16a/16
1 = a
The value of a = 1. Since it is a positive number, then it confirms that the parabola opens upward.
Therefore, the quadratic function in vertex form is:
f(x) = (x + 4)^2 + 3
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Related Questions
What’s the answer to this question
Answers
Answer:
-9 and -8 ...............
Use the 1st derivative test to find the intervals where the function is increasing or decreasing. Please show your work so I can get a better understanding on how you achieved the solution. Thank you.
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As the name of the test suggests, you have to compute the derivative:
[tex]f(x) = \dfrac1{2x+3} \implies f'(x) = -\dfrac2{(2x+3)^2}[/tex]
Find where, if at all, the derivative vanishes or is undefined - these are the critical points of f(x).
In this case, the derivative is never 0 since the numerator is constant and the denominator is non-negative. You also see that f '(x) is negative over its entire domain.
The denominator goes to 0 when 2x + 3 = 0, or x = -3/2.
Now split up the domain of f(x) into intervals with endpoints at the critical points. Here, we consider the two intervals, (-∞, -3/2) and (-3/2, ∞).
Take any point from either interval and check the sign of f '(x) at that point. Any points will do, but you should strive to pick one that makes calculations simple.
• From (-∞, -3/2), take x = -2; then f ' (-2) = -2 < 0. Since f '(x) is negative over this interval, f(x) is decreasing over it.
• From (-3/2, ∞), take x = 0; then f ' (0) = -2/9 < 0. Again, this means f(x) is decreasing over this interval.
So, the first derivative test tells us that f(x) = 1/(2x + 3) is decreasing over the intervals (-∞, -3/2) and (-3/2, ∞); in other words, over its entire domain.
For the second function, we have
[tex]f(x) = \dfrac{x+1}{x+3} \implies f'(x) = \dfrac{(x+3)-(x+1)}{(x+3)^2} = \dfrac2{(x+3)^2}[/tex]
Again, there's only one critical point, this time at x = -3 where the derivative is undefined.
• From the interval (-∞, -3), take x = -4; then f ' (-4) = 2 > 0, so f(x) is increasing.
• From the interval (-3, ∞), take x = 0; then f ' (0) = 2/9 > 0, so f(x) is increasing.
Find the equation of the line through the points (−2,5) and (4,9).
Enter your answer in standard form Ax+By=C, where A is a positive integer, and B and C are integers.
Answers
9514 1404 393
Answer:
2x -3y = -19
Step-by-step explanation:
Taking the differences between the given points, we have ...
(Δx, Δy) = (4, 9) -(-2, 5) = (6, 4)
The equation of the line can be written ...
Δy·x -Δx·y = Δy·(x1) -Δx·(y1) . . . . . for point (x1, y1) on the line
4x -6y = 4(-2) -6(5) = -38
Dividing by 2 gives the standard form equation ...
2x -3y = -19
_____
Additional comment
The original equation 4x-6y=-38 satisfies the requirements of this problem. However, "standard form" requires the numbers in the equation be mutually prime (in addition to the problem requirements). That is, they must have no common factors. Hence, we must remove the common factor of 2 in order to have true "standard form."
Help help help please please
Answers
Answer:
23×24 =27
answer is 7
answer is 7
Answer:
Step-by-step explanation:
[tex]a^{m}*a^{n}= a^{m+n}\\\\\\\dfrac{a^{m}}{a^{n}} = a^{m-n}\\\\\\2^{3}*\dfrac{2^{5}}{2^{1}}=2^{3}*2^{5-1}\\\\=2^{3}*2^{4}\\\\=2^{3+4}\\\\=2^{7}[/tex]
It is estimated that each guest at a party will eat 9/10
pounds of chocolates. How many guest can be served with 27 pounds of chocolate?
Answers
Answer:
30 guests
Step-by-step explanation:
If each guest eats 9/10 lbs of chocolate, then they eat 0.9 lbs of chocolate. We have 27 lbs of chocolate to be eaten.
To solve this, simply:
[tex]\frac{27}{.9} =30[/tex]
where 27 lbs is divided by 0.9lbs per guest to equal 30 quests.
I hope this helps!!! :)
) What is 35% of 10?
0.35(10)
Answers
Answer:
3.5
Step-by-step explanation:
35% of 10 is the same thing as 0.35(10)
0.35 x 10 = 3 + (0.05 x 10) = 3 + 0.5 = 3.5
-Chetan K
A(n) _____ is a proof that uses algebraic properties to reach a conclusion about an algebraic equation.
Answers
Answer:
algebraic proof
The complete statement is -
"An algebraic is a proof that uses algebraic properties to reach a conclusion about an algebraic equation"
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement as -
"An _____ is a proof that uses algebraic properties to reach a conclusion about an algebraic equation"
The complete statement is -
"An algebraic is a proof that uses algebraic properties to reach a conclusion about an algebraic equation"
Therefore, the complete statement is -
"An algebraic is a proof that uses algebraic properties to reach a conclusion about an algebraic equation"
To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ6
If someone build a house for 50 years how many months did it take to complete
Answers
Answer: 600
Step-by-step explanation: 12 months in one year. 12x50=600 months
Answer:
600 months
Step-by-step explanation:
In 1 year there are 12 months, so we take 50 (the years) and multiply that by 12
50x12=600 and we fact check by 600÷12=50. It takes 600 months to build the house over 50 years.
Please help
Explain the significant of the arithmetic
modulo in solving problems then support your answer with examples.
Answers
Answer:
A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in 7 + 8 = 15, but clocks "wrap around" every 12 hours.
Step-by-step explanation:
hope It's can help
Are the ratios of 3 apples to 5 oranges and 9 apples to 15
oranges equivalent? Why or why not? Explain
Answers
Answer:
yes they are equivelant
Step-by-step explanation:
the reason they are equivelant is because they go from 3 apples to 6 apples to 9 apple, and 5 oranges to 10 oranges to 15 oranges. so this mark's it is also tymced by three
Evalute: -|-x+2| for x = -3
Answers
the answer is -5
The number of hours Darla baby - sat her sister each week for the last 12 weeks is shown below
Answers
Answer: the box and whisker plot looks like this, the pink line starts between 8 and 10, the box starts between 10 and 12, the middle is between 14 and 16, the right side of the box is between 18 and 20, and lastly the pink line on the right ends at 22.
Step-by-step explanation: I did the test
Can anyone help please:)
Answers
Answer:
THEORTICAL PROBABILITY:
1A) F
1B) B
1C) A
1D) D,E,F
2A) R
2B) B
3A) odd number
3B) No, same.
3C) less than 5
================
1A) 8/30=4/15
1B) 10/30=1/3
1C) 12/30=2/5
1D) 18/30=3/5
1E) 22/30=11/15
1F) 22/30=11/15
2A) 3/8
2B) 1/8
2C)4/8=1/2
2D) 5/8
2E)3/8
3A) 50
3B) 150
3C) 250
3D) 100
3E) 100
Step-by-step explanation:
Help I was absent when she taught this
Answers
Answer:
b
Step-by-step explanation:
A gallon of apple juice is
$7. A pack of eight 4.23
oz box apple juice is
$2.39. Which is a better
deal?
Answers
What is the x intercept of f(x) = x + 12
Answers
Answer:
-12
Step-by-step explanation:
Clayton wants to be a musician. After school one afternoon, he spends half his time practicing his drums and 3/4 of the remaining time on homework and dinner. He spends the remaining 3/4hour talking with and texting his friends. How long did he practice the drums?
Answers
Answer:
x - x/2 - (x/2)(3/4) - 3/4 = 0
x = 6
so, he spent 3 hours on the drums.
If you can answer this right i'll mark you brainiest
Answers
Answer:Think of the equation as an equation for a line
y=mx+b
where in this case
C= 5 /9 (F−32)
or
C= 5 /9 F - 5/9 x 32
You can see the slope of the graph is 5 /9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5 /9 of 1 degree Celsius.
C= 5 /9 (F)
C= 5/9(1)
C=5/9
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9/5 degrees Fahrenheit.
C= 5/ 9 (F)
1= 5 /9 (F)
(F)= 9 /5
Since
9/5 = 1.8, statement II is true.
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5/9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C= 5 /9 (F)
C= 5 /9 x 5/9
C=25/81
(which is≠1)
An increase of 5/9
degree Fahrenheit leads to an increase of
25/81.
, not 1 degree, Celsius, and so Statement III is not true.
The final answer is D.
A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85 Adult tickets are $15 each and tickets are $5 each. Let X represent adult tickets. Let y represent child tickets Write an equation to model the total amount of money that they spent.
Answers
9514 1404 393
Answer:
15x +5y = 85 . . . . . equation for money spent
Step-by-step explanation:
The money spent will be the sum of products of numbers of tickets and their cost:
15x +5y = 85
__
The number of tickets bought will be the sum of the numbers of each kind.
x +y = 13
_____
The solution of this system of equations is (x, y) = (2, 11).
Find the slope intercept form of the equation of the line that’s has the given properties (1 , 3) m=1/4
Answers
Answer:
y = 1/4x + 11/4
Step-by-step explanation:
Given the slope, m = 1/4, and the point, (1, 3):
We can substitute these values into the slope-intercept form, y = mx + b, in order to solve for the y-intercept.
The y-coordinate (b) of the point, (0, b ) is the y-intercept of the line where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.
y = mx + b
3 = 1/4(1) + b
3 = 1/4 + b
Subtract 1/4 from both sides:
3 - 1/4 = 1/4 - 1/4 + b
11/4 = b
The y-coordinate, b, of the y-intercept is 11/4.
Therefore, the slope-intercept form is: y = 1/4x + 11/4
Please mark my answers as the Brainliest if you find this explanation helpful :)
I'll give brainliest please help
graphing
both of them please
Answers
Step-by-step explanation:
It's easier to graph when both equations are in its slope-intercept form, y = mx + b.
System 1: -3x -15y = 15-2x -10y = 10-2x -10y = 10
-2x + 2x - 10y = 2x + 10
-10y = 2x + 10
-10y/-10 = (2x + 10)/-10
y = -1/5x -1 [slope: -1/5, y-intercept (0, -1)]
-3x -15y = 15
-3x + 3x - 15y = 15
-15y = 3x + 15
-15y/-15 = (3x + 15)/-15
y = -1/5x - 1 [slope: -1/5, y-intercept (0, -1)]
To graph this system, plot the y-intercept, (0, -1) on the graph, then use the slope, m = -1/5 (down 1 unit, run 5 units to the right). Repeat the process until you have enough points to connect and create a line.
Because the given systems of linear equations are equivalent, their lines coincide on top of each other. This means that they have infinitely many points of intersection. Hence, they have infinite solutions.
System 2: 8x + 6y = 244x + 3y = 98x + 6y = 24
6y = -8x + 24
6y/6 = (-8x + 24)/6
y = -4/3x + 4 [slope: -4/3, y-intercept (0, 4)]
4x + 3y = 9
3y = -4x + 9
3y/3 = (-4x + 9)/3
y = -4/3x + 3 [slope: -4/3, y-intercept (0, 3)]
Use the same techniques as described in the first part. Plot the y-intercepts on the graph, then use the slope of each equation to plot other points.
These lines are parallel, which implies that they will never intersect each other. Hence, there's no solution to this system.
Attached are the screenshots of the graphed systems of linear equations.
Help me please express the simplest radical form
Answers
Answer:
The answer is 8√2
Hope this helps
Is (–2, –9) a solution to the equation y = x + 7
Answers
Answer:
no
Step-by-step explanation:
the opposite number of -6.1
Answers
Answer:
I'm pretty sure that would be 6.1 - considering negative numbers and positive numbers are opposites.
Please help me with this problem.
Answers
Answer:
yes
no
yes
no
Step-by-step explanation:
You can tell it's negation when the word "not" is used.
A 24-pack of mini cans of soda cost $21.98. How much iseach can?
Answers
Jacob went bowling over the weekend. On Saturday, he bowled at Bowlero, where he
rented shoes for $3.25 and paid $3.75 for each game. On Sunday, he bowled at the
Cowtown Bowling Center, where he rented shoes for $2.50 and paid $4.00 per game.
If he spent the same amount each day, how many games did he bowl? (Let the
number of games played = 2.)
Answers
Answer:
3 games played every Day
Step-by-step explanation:
So for Cowtown Bowling Center the cost of shoes is $2.50, and $4.00 per game
Then the Bowler is $3.25 for shoes and 3.75 per game
So to get the answer your gonna wanna set up the equation like
Saterday =$3.25+$3.75(x), then for
Sunday = $2.50+$4.00(x)
The X is how many games so if you plug in the same amount of game in both
Example
Saterday=$3.25+$3.75(2)=$10.75
Sunday = $2.50+$4.00(2)=$10.50
So if you do 3 then the totals will come out to be the same
Answer
Saterday=$3.25+$3.75(3)=$14.50
Sunday = $2.50+$4.00(3)=$14.50
Patricia visited a friend who lives 120 miles away. On her way there she averaged 60 mph. On the way back, she only averaged 40 mph. What was the total amount of time she spent driving?
Answers
Answer:
5 hours
Step-by-step explanation:
120/60= 2
120/40= 3
3+2=5
Please help Please help Please help Please help Please help Please help
Answers
Answer:
the answer is b
Step-by-step explanation:
-3x + y = 10
solve the equation for Y
Answers
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-3*x+y-(10)=0
Pull out like factors :
-3x + y - 10 = -1 • (3x - y + 10)
y = 3x+ 10