Answers
Vertex is (2,3), so that gives us:
y=a(x-2)^2+3
Now the graph goes through (0,1), so plug that in to find a:
1 = a(0-2)^2+3
-2 = a(-2)^2
-2 = a•4
-1/2 = a
So, y = -1/2 (x-2)^2 + 3
Answer:
y = - ½(x - 2)² + 3
Step-by-step explanation:
Given the vetex, (2, 3), as the maximum point on the graph, along with the y-intercept, (0, 1):
We can substitute these values into the given vertex form of the quadratic equation:
y = a(x - h)² + k
where:
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. If 0 < a < 1, the graph is wider than the parent function. If a > 1, the graph is narrower than the parent function.(h, k ) = vertexh = determines how far left or right the parent function is translated.k = determines how far up or down the parent function is translated.Use vertex = (2, 3) and y-intercept (0, 1) to solve for "a":
y = a(x - h)² + k
1 = a(0 - 2)² + 3
1 = a(-2)² + 3
1 = a(4) + 3
Subtract 3 from both sides:
1 - 3 = a(4) + 3 - 3
-2 = 4a
Divide both sides by 4 to solve for a:
-2/4 = 4a/4
- ½ = a
Therefore, the value of a = - ½. This means that the graph opens downward, and that the parabola is wider than the parent function.
The quadratic equation in vertex form given a = - ½, and vertex (2, 3) is:
y = - ½(x - 2)² + 3
Please mark my answers as the Brainliest if you find this explanation helpful :)
Related Questions
Ariadne jogs at an average speed of 8 km/h. How far does she travel in 1½ hours?
Answers
Answer:
12km
Step-by-step explanation:
1 hour = 8 half hour = 4
8+4=12
Factor the expression using the common factor −4 .
−12x+2.4y−48
Drag a value or operation/sign to the boxes to correctly factor the linear expression.
Answers
Answer:
-4( 3x - 0.6y + 12)
Step-by-step explanation:
The expression - 12x + 2.4y - 48 taken a common factor of - 4 we have
- 4(3x - 2y + 12).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
The common factor on the other hand is the highest possible value that we can divide each of the given terms.
Given, - 12x + 2.4y - 48.
- 12x + 8y - 48.
Taking - 4 as the common factor we'll have
- 4(3x - 2y + 12).
learn more about common factors here :
https://brainly.com/question/11221202
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50×54+23-44+66 Simplification no spam steps must
Answers
Answer:
=2745
Step-by-step explanation:
=2700+23−44+66
=2723−44+66
=2679+66
=2745
I need helpp plz I will mark brainliest and i will follow but plz help me
Answers
Answer:
up 5 and 1.5 and -6 and 6 (if im not mistaking)
Step-by-step explanation
what is z in -5/2 = 3/4z + 1/2? please also explain the steps i’m really confused
Answers
Subtract 1/2 to both sides of the equal sign
-6/2=3/4z
Now to get Z By itself we will do inverse property and multiply both sides of the equal sign by 4/3
Z=-4
Anyone help me please?
Answers
Each rhombus has four right angles-False
Each square has four right angles-True
3. What is the hypothesis of the following conditional statement?
Conditional Statement: If two angles form a right angle,
then they are complementary.
Two angles form a right angle.
They are complementary.
If two angles are complementary, then they form a right angle.
The angles are adjacent.
Answers
Answer:
A: Two angles form a right angle.
Step-by-step explanation:
took the test
Answer:
Two angles form a right angle.
Step-by-step explanation:
The first part of the statement, the condition that must be met, is the hypothesis.
Please help me do it
Answers
Step-by-step Explanation:
We are going to solve this problem using integration by parts. We can write the integrand as
[tex]\dfrac{4x}{x^2+4x+3} = \dfrac{4x}{(x+3)(x+1)}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{A}{x+3} + \dfrac{B}{x+1}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{Ax + A + Bx + 3B}{x^2+4x+3}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:=\dfrac{(A+B)x + (A+3B)}{x^2+4x+3}[/tex]
Comparing the above term to the left hand side, we can see that
(A + B)x = 4x
A + 3B = 0
Solving for A and B, we find that A = 6 and B = -2 so our integrand becomes
[tex]\dfrac{4x}{x^2+4x+3} = \dfrac{6}{x+3} - \dfrac{2}{x+1}[/tex]
We can now easily integrate this expression as follows:
[tex]\displaystyle \int{\dfrac{4x}{x^2+4x+3}}dx = 6\int{\dfrac{dx}{x+3}} - 2\int{\dfrac{dx}{x+1}}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:= 6\ln|x+3| - 2\ln|x+1| + C[/tex]
I am kindly a lost help
Answers
Answer:
First of all this is a negetive slope so it goes down and its y-intersect is -4
and it is a slope of -8/6 or -1 2/3
So the slope is
-8/6-4
Hope This Helps!!!
Find the distance between the two numbers on the number line, -4 7/12 and -3 1/6.
Answers
Answer:
1 1/2
Step-by-step explanation:
Eduardo had some
bubble tape. He gave 5
⅙ feet to his friends and
now he has 2 ¼ feet left.
How much bubble tape
did Eduardo start with?
first correct answer gets brainlist
Answers
Answer:
7 5/12 feet of tape
Step-by-step explanation:
Find the LCM and add the fractions in this case is 12
Find the unit price of the pens and round to the nearest tenth if necessary
Answers
Answer:
The answer is .21
Step-by-step explanation:
$3.15÷15=.22
Kennedy is making dessert for Thanksgiving.
She decides to make thirteen pumpkin pies. To
make each of the 13 pies she is baking she will
need 12 cups of pumpkin, 4 cups of sugar, and
1 cup of milk. How many cups of pumpkin will
Kennedy need to make all her pies?
Answers
Answer:
156 cups
Step-by-step explanation:
The most important info in this problem are for every 1 pie, she needs 12 cups of pumpkin. So do 13 pies x 12 cups = 156 cups of pumpkin.
Can someone help me solve this
Answers
Answer:
Constant of proportionality = 1/3
y = 1/3a
Step-by-step explanation:
Constant of proportionality: k = y/x
k = 1/3
k = 4/12 = 1/3
An aquarium is creating a display of a shark that has 100 teeth in each row. The aquarium can buy shark teeth for $10 each. How much will the aquarium spend on shark teeth to create the model?
Answers
Answer:10,000
Step-by-step explanation:10x100=1000
(b) If you have budgeted $20 for a cab ride to tour the downtown area, how far can you go? Set up and solve an equation.
Round your answer to two decimal places.
If you have budgeted $20 for a cab ride to tour the downtown area, you can go miles.
Answers
Answer:
15 miles
Step-by-step explanation:
River Fun Boats rents paddle boats. The euqation C = 0.10t + 4 gives the charge in dollars, C, for renting a paddle boat for t minutes. A customer paid $9.00 for their rental. How lond did the customer use a paddle boat?
Answers
Answer:
Step-by-step explanation:
9 = 0.10t + 4
5 = 0.10t
t = 50 minutes
Help me with this lol
Answers
Answer:
13
Step-by-step explanation:
5+3+5=13
PLEASE SOME ANSWER QUICKLY!!!!
Answers
×2 multiple with 2
D
enjoy me hard work
PLS HELP REAL ANSWERS ONLY
Answers
Answer:
(0;2), maximum
Step-by-step explanation:
I dont know.. Please anwser this
Answers
If k and l are parralel, that means if you move them to each other, or shift k, you will get the same angle as ABC. Thus, it's still going to be 19 degrees.
Hey can anyone help with this problem pls and ty !
Answers
Step-by-step explanation:
(x + 20)º and (4x - 5)º are supplementary angles, meaning the sum of their angles = 180º.
(x + 20) + (4x - 5) = 180
5x + 20 - 5 = 180
5x + 15 = 180
5x = 165
165/5 = 33
Answer: x = 33
4n > with the line under it 20. Plot on number line
Answers
Answer:
5
Step-by-step explanation:
divide 4 by both numbers
If the graph of equation 2x+ky=10k, intersect x-axis at point (5,0).Find the value of K
Answers
Answer:
K= 1
Step-by-step explanation:
The line of AOB intersects the graph at the x-axis at point (5,0)
(5,0)=(x,y)| (x=5, y=0)Soooo...
2x+ky=10k2(5)+k*0=10k10=10kk=10/10k=1- 3 7/9 - 1 2/9
What is this answer
Answers
Answer:
-5
Step-by-step explanation:
(-3 7/9) - 1 2/9 = -5
Hope this helps :)
Pls make brainliest :3
And have an amazing day <3
Answer:
-5
Step-by-step explanation:
Since the signs are alike, we add and then take the sign
-(3 7/9 + 1 2/9)
-(4 9/9)
-(5)
What is the x value such that y =15 - 3x and y = 0?
Answers
0 = 15 - 3x
Subtract 15 from both sides
0 - 15 = -3x
Simplify
-15 = -3x
The negatives cancel out:
15 = 3x
Divide by 3 on both sides
5 = x
Divide the difference between 1,000 and 200 by 4
Answers
Answer:
200
Step-by-step explanation:
1,000-200=800
800/4=200
Answer:3200
Step-by-step explanation:
1000 subtracted by 200 =800
multiply 800 by 4 =3200
Find the distance between the points.
(-1, 1), (3, -2)
Answers
Distance = 5
Step-by-step explanation:
√[(x₂ - x₁)² + (y₂ - y₁)²]
√[(3 - (-1))² + (-2 - 1)²]
√[4² + -3²]
√[16 + 9]
√25
5
One number exceeds another by 6 and their sum is 16. Find the two numbers.
Answers
Answer:
answer is 11 or 5
Step-by-step explanation:
x+y=16 ------ 1
x-y= 6 ------ 2
______
2x = 22
x =22/2 =11
put the value of x on equation 1
x+y =16
11+y =16
y =16-11 =5
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answers
Answer:
infinitely many solution
Step-by-step explanation:
Answer:
Any value of x makes the equation true.
All real number
Interval Notation:
(−∞,∞) So it's Infinitely many solutions.