Answers
Answer:
Option 1: y = (x - 2)² + 2
Step-by-step explanation:
Given the vertex, (2, 2), of an upward-facing parabola, and using the y-intercept of the graph, (0, 6):
Definitions:The vertex form of the quadratic equations is:
y = a(x - h)² + k
where:
(h, k) is the vertex.
The value of h represents the horizontal translation of the graph. h > 0 represents the horizontal shift of the graph h units to the right. h < 0 shifts the graph |h | units to the left. The value of k represents the vertical translation of the graph. k > 0 shifts the graph k units upward. k < 0 shifts the graph |k | units down.The sign of a determines the direction of the graph's opening. The value of a also determines the vertical stretch or shrink of the graph.
If a is positive (or a > 1), then the graph opens upward. The value of a > 1 also represents the vertical stretch of the graph. If a is negative (or a < 0), then the graph opens down.The value of 0 < a < 1 represents the vertical shrink or compression of the graph. Solution:Substitute the values of the vertex (2, 2) and the y-intercept, (0, 6) into the vertex form to solve for the value of the coefficient, a:
y = a(x - h)² + k
6 = a(0 - 2)² + 2
6 = a(-2)² + 2
6 = 4a + 2
Subtract 2 from both sides
6 - 2 = 4a + 2 - 2
4 = 4a
Divide both sides by 4 to solve for a :
[tex]\displaytext\mathsf{\frac{4}{4} \:=\frac{4a}{4}}[/tex]
a = 1
Quadratic Equation in Vertex Form:Therefore, given the vertex, (2, 2) and a = 1, the quadratic equation in vertex form is: y = (x - 2)² + 2, thereby matching Option 1.
Related Questions
What’s the remainder of 3,231 / 7
Answers
The time, t, it takes a runner to cover a specified distance is inversely proportional to the runner's speed. If Jann Avery runs at an average of 6 miles per hour, she
will finish a race in 2. 1 hours. How long will it take Jackie Donofrio, who runs at 4 miles per hour to finish the same race?
Answers
To solve this problem you will need this tool, it is the formula of speed :
speed = distance/time
(I suggest you to remember this one for life, it is a really useful one)
Let's check how long that Jackie nice dude will take to finish the race...
Jann avery runs at an average of 6 mph (miles per hour), so we already got the speed for our formula. And she will finish the race in 2.1 hours so we got the time. What do we miss ? The distance.
Let's write what we already know to solve this puzzle :
6 = d / 2.1
Where d is that unknown distance.. So we are in front of an equation here let's solve it :
d / 2.1 = 6
d = 6 * 2.1
d = 12.6 miles
Now that we know that distance, for the race, we can see if that poor Jackie Donofrio has all his chances to catch Jann Avery...
We already know his speed... and since we have the distance, we write :
4 = 12.6 / t
Where t is the unknown time, for Jackie, to finish the same race. Let's solve the equation :
4t = 12.6 (we multiplied t on each side of the equation)
t = 12.6 / 4
t = 3.15
Jackie Donofrio, who runs at 4 miles per hour, will finish the race in 3.15 hours
Good Luck
What number should go in the space?
Multiplying by 0.51 is the same as decreasing by _____%.
Answers
Answer:
49
Step-by-step explanation:
x multiplied by 0.51 is the same as 49% of x
The expression 3(x + 4) - (2x + 7) is equivalent to
Answers
Answer:
Why don't know wt is equal to..
Step-by-step explanation:
3(x + 4) - (2x + 7)
3x + 12 - 2x - 7
1x + 5
x + 5
6(4x-3)-9x distributive property
Answers
Answer:
15x-18
Step-by-step explanation:
use pemdas
do parenthesis first
6(4x-3)-9x
24x -18 -9x
15x-18
The simplified expression after applying the distributive rule for the expression 6(4x - 3) - 9x becomes 15x - 18
The given expression is:
6(4x-3)-9x
Expanding the expression using the distributive rule
24x - 18 - 9x
Collect like terms
24x - 9x - 18 (since 24x and 9x are similar)
The resulting expression becomes:
15x - 18
The simplified expression after applying the distributive rule for the expression 6(4x - 3) - 9x becomes 15x - 18
Learn more on distributive property here:
https://brainly.com/question/4077386
What is the equation of this line *
Answers
Answer:
I would have to see the line to answer the question.
Josh runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
Answers
Answer:
2.8 milesStep-by-step explanation:
Josh runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
7 : 60 = x : 24
x = 7 * 24 : 60
x = 2.8 miles
Write the Equation
Equation
X Y
-2 5
-1 3
0 1
1 -1
y=-X+2
y=x+2
y=2x+1
y-2x+1
Answers
Answer:
y=-5×+13
Step1 inter change ×gy
For the problem -4(-5)(9), will the answer be positive or negative?
Answers
Answer:
Positive
Step-by-step explanation:
-4(-5)(9)
Negative cancels out negative, so it makes a positive:
20(9)
Simplify normally to get 180 as your final answer.
Question is below!!! 9 and 10!!!! Pls help
Answers
Answer:
9. 1.75 m/s²; 8 s
10. (12 6/7) °/s; (10 5/7) kt/s
Step-by-step explanation:
Acceleration is the change in velocity divided by the change in time.
__
9.(22 m/s -15 m/s)/(4 s) = 7/4 m/s² = 1.75 m/s²
The eagle's average acceleration is 1.75 m/s².
__
The relation can also be used to find the time for a given change:
a = Δv/Δt ⇒ Δt = Δv/a
Δt = (22 m/s -8 m/s)/(1.75 m/s²) = 8 s
It would take the eagle 8 seconds to go from 8 m/s to 22 m/s.
__
10.From north to south is a direction change of 180°. Then the rate of change is ...
a = 180°/(14 s) = 12 6/7 °/s
__
From 75 knots north to 75 knots south (-75 knots, using north as a reference) the magnitude of the average acceleration is ...
|-75 kt -75 kt|/(14 s) = 150/14 kt/s = 10 5/7 kt/s
Lyndon got a new job which pays $24.25 per hour. He works 40 hours per week. He pays 5% state income tax on his earnings. How much does Lyndon have remaining after state income tax is deducted from 4 weeks of pay?
Answers
Answer:
$3686 remaining after tax
Step-by-step explanation:
Expand the following expression.
Answers
Answer:
C. [tex]\frac{39}{4}[/tex]x +[tex]\frac{39}{16}[/tex]
Step-by-step explanation:
distribute
Answer:
(39/4)x + 39/16
Answer C
Step-by-step explanation:
(13/4) * 3x + (13/4) * (3/4)
(39/4)x + 39/16
5(4 - 1)
The Second person to answer gets Brainliest
Answers
Answer:
the answer is 15 because you have to do the problem in the parentheses first then multiply by 5
Which statement is true
Answers
Answer:
[tex]xv=yu[/tex]
Step-by-step explanation:
You can simplify the equation by cross multiplying, or doing it the more 'correct' way that some teachers way want:
[tex]\frac{x}{y}=\frac{u}{v}[/tex]
Multiply both sides by y:
[tex]x=\frac{yu}{v}[/tex]
Then multiply both sides by v:
[tex]xv=yu[/tex]
That's one of your answer options, so no need to do anything else.
Write 10 10 10 10 10 with an exponent.
Answers
Answer:
10 5 ( Exponent )
Hope it helps
What is the quotient of 9198 and 14?
Answers
Answer:
656.36
Step-by-step explanation:
you just divide then have to round the decimal point to 36
The perimeter of an equilateral triangle is 24 cm. Find the length of each sides
Answers
Answer:
8cm
Step-by-step explanation:
An equilateral triangle means that all the sides are equal (the same length). A triangle has 3 sides so all we have to do is:
24/3 = 8
Each side is 8cm long
Answer:
Length of each sides = 8 cm
Step-by-step explanation:
Given the perimeter of an equilateral triangle, 24 cm:
Equilateral triangles have three congruent sides.
Hence, to find the length of an equilateral triangle, simply divide the perimeter by 3 (since an equilateral triangle has three equal sides).
Perimeter of an equilateral triangle = 24 cm
Side = 24 cm ÷ 3 = 8 cm
Therefore, the length of each side is 8 cm.
x^2-4x+11
In the form a(x+h)^2+k
Answers
Answer: im very sorry
Step-by-step explanation:
Ray uses 1/4 of a gallon of gasoline to drive a distance of 5 1/2 miles. At this rate, how many miles can he drive on 1 gallon of gas?
Any help is appreciated!
Answers
Answer:
22
Step-by-step explanation:
Can someone tell me which one is the answer? Am I wrong or correct?
Answers
Answer:
I don't believe your wrong mate
Help would be greatly appreciated!!
Multiply as indicated. Write the product in standard form.
(1+3i)(-3-i)
Thanks to whoever helps in advance!!
Answers
Answer:
-10i
Step-by-step explanation:
-3-i-9i+3
remove the Opposites
collect like terms
-i-9i
=-10i
Sandra baked 9 pies that weigh 81/4 pounds total. How much does each pie weigh?
Answers
Answer:
2 1/4 ×9
= 9/4 ×9
= 81/4
= 20 1/4
Step-by-step explanation:
81/4/9
= 81/4 × 1/9 (Reciprocal)
= 9/4 pounds
= 2 1/4 pounds
Answer:
11/12 lb
Step-by-step explanation:
I think you mean 8 1/4 lb.
(8 1/4)/9 = 33/4 × 1/9 = 33/36 = 11/12
Answer: Each pie weight 11/12 lb.
What time does the clock show?
12
11
1
10
2
9
3
8
4
7
6 5
Answers
Answer:
5:20
Step-by-step explanation:
In order to tell the time on an analog clock, we start by looking at the hour (shorter) hand. On this clock, it is pointing between the 5 and the 6, so we know it's a little after 5 o'clock.
Next, we look at the minute hand. Each number on the clock represents five minutes past the hour and the minute hand is pointing at the 4, so we know it is 4 x 5 or 20 minutes past the hour.
Therefore, we know that the time is 20 minutes after 5, or 5:20.
The time shown on the clock, obtained by reading the clock is; 5 : 20
How does one read a clock?Reading an analog clock involves looking at the positions of the clock's hands to determine the time.
The long hand, which is the minute hand of the clock is pointing at the number 4, which indicates that the time is 20 minutes past the hour, because each number on the clock face represents 5 minutes; (4 × 5 = 20). The direction the short hand, which is the hour hand is past the number 5, it indicates that the time is past 5 o'clock.
The position of the hour hand between 5 and 6 indicates that the time shown on the clock is 20 minutes past 5; 5 : 20
Learn more on reading clocks here: https://brainly.com/question/30202307
#SPJ2
Can you help me I can’T play in my game Sunday if I don’t pass
Answers
Answer:
Option D is the correct answer. The last one.
Hope it helps you...
Please mark as brainlliest!!!
brainly helpppp me out
Answers
Answer:
D
Step-by-step explanation:
I think it might be (D) $2x-5
5. What percent of 36 is 24?
A. 50%
B. 66.7%
C. 75%
D. 80%
Answers
Answer: B. 66.7%
Step-by-step explanation:
Divide 24 by 36:
24/36 = 2/3
B. 66.7%
Answer:
answer is B I just had the test
Step-by-step explanation:
Ezra and Benji are playing the game with Harrison. After Ezra doubles his hand's value, he has a total of -12.5 points. What was his hand's value before
he doubled it?
Answers
half of -12.5 is -6.25
What are the values of m and n
Answers
Answer:
m = 20°, n = 45°Step-by-step explanation:
Both of the triangles are isosceles as marked on the diagram.
The right triangle has missing angles of:
n = 90°/2 = 45°The missing angles of the bigger triangle:
m + n = 1/2(180° - 50°)m + 45° = 65°m = 20°The temperature was -16 degrees at noon. By 2:00 PM it dropped to 10 Degrees. What was the temperature at 2:00 Pm
Answers
2x+5=12 i don´t know what the value of x is
Answers
Answer: X = 7/2 or 3.5