Answers
Answer:
f(x) = 3(x - 2)² + 4
OR
f(x) = 3x² - 12x + 16
Step-by-step explanation:
Vertex form of a parabola:
y = a(x - h)² + kStandard form of a parabola:
y = ax² + bx + cLet's find the vertex of this parabola.
(h, k) → (2, 4)In order to find the a-value (vertex form), let's use another point besides the vertex on the parabola.
Using (3, 7) for (x, y), let's substitute this point and the vertex (2, 4) for (h, k) into the vertex form equation and solve for a.
7 = a[(3) - (2)]² + 4Simplify using PEMDAS.
7 = a(1)² + 47 = a + 4Subtract 4 from both sides.
a = 3Now we have (h, k) and a of the vertex form.
y = a(x - h)² + k → y = 3(x - 2)² + 4In order to convert from vertex to standard form, simplify the equation by FOILing.
y = 3(x - 2)² + 4y = 3(x² - 4x + 4) + 4Distribute 3 inside the parentheses.
y = 3x² - 12x + 12 + 4Combine like terms.
y = 3x² - 12x + 16Therefore, we have the answer:
Vertex form:
f(x) = 3(x - 2)² + 4Standard form:
f(x) = 3x² - 12x + 16Related Questions
A student observes a difference in the activity level of fish at a pet store. The fish in an aquarium near the window are swimming around more quickly tha the fish in an aquarium placed in the back of the store. The student forms a hypothesis about the effect of sunlight on fish activity levels and arranges to conduct an experiment. Which variable could be an independent variable in the student's experiment? types of fish sold speed of swimming fish amount of time fish were active temperature of water in fish tank
Answers
Answer: Types of fish sold
The type of fish sold is the independent variable in the student's experiment. So, the correct option is (A).
What are Variables?
A variable is any kind of characteristic, number, or quantity which can be measured or counted. It can also be called a data item. Examples of variables are age, sex, occupation income and expenses, country of birth, capital expenditure, class grade, eye color, and vehicle type.
There are two types of Variables are:
1. Dependent variable
A dependent variable is a type of variable which changes as the result of independent variable manipulation which is the outcome interested in measuring, and it "depends on" the independent variable.
2. Independent variable
An independent variable is the type of variable which is manipulated or varied in an experimental study in order to detect its effects. This is "independent" because it is not affected by any other variable in the study.
In above case, this is independent because types of fish characteristic is not dependent for the experiment.
Thus, the type of fish sold is the independent variable in the student's experiment. So, the correct option is (A).
Learn more about Variables, here:
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Find the length of side A
Answers
Answer:
D) 4
Step-by-step explanation:
can somebody good at math help me with these please I would really appreciate it
Answers
Answer:
down below:)
Step-by-step explanation:
sale price discount
1. multiplied by 0.82
2. multiplied by 0.75
3. multiplied by 0.9
1. 18.45
2. 30
3. 23.4
It costs $60 to reserve a movie theater for a party. There is also a charge of $3 for each person. Which expression represents the total cost to reserve a movie theater for n persons?
Answers
Can you guys help me ;) first person to help will get brainlist
Answers
the measurements have little difference, so it will be very close to an equilateral rather a right triangle.
Write 5^3 as a product of the same factor.
Answers
Answer:3*3*3*3*3=243
Step-by-step explanation:
(Exponential Models)
a.) Suppose you invest $500 in a savings account that pays 3.5% annual interest. How much will be in the account after 5 years?
$_ _ _ . _ _
b.) Suppose you invest $500 in a savings account that pays 3.5% annual interest. When will the account contain at least $650?
After _ years.
Answers
B- same thing just add then divide
227.4 + 213.5
513.9 – 46.1
348.2 + 62.8
637.9 – 206.3
Answers
Step-by-step explanation:
227.4 + 213.5 = 440.9
513.9 – 46.1 = 467.8
348.2 + 62.8 = 411
637.9 – 206.3 = 431.6
Answer:
1: 440.9
2: 467.8
3: 411
4: 431.6
Hope this helps.
Answer:
1. 440.9
2. 467.8
3. 411
4. 431.6
Step-by-step explanation:
Rearrange x = 3g + 2 to make g the subject g=?
Answers
Step-by-step explanation:
x=3g+2
you need to move the equation to the other side, first you'd start with the one furtherest from g, which is is 2.
x = 3g
-2. - 2
and minus it from both sides
x-2=3g
3g is like 3x, which is 3 times x and you need to use the opposite operators so times would become divide.
so now it becomes x-2 over 3=g
find the measurement indicated in each parallelogram first one says 60 and second says 79 please help !
Answers
Answer:
1. 60+X=180(adjacent angles of parallelogram)
X=120
2. X=79(opposite angles of parallelogram)
Angles P and R are congruent so
P & R both have a value of 60°
60x2= 120°
360-120=240° are left
Angles S and Q are also congruent so divide 240 by two
240/2=120°
Answer 1.)Q=120°
Again it equals 360° total
Angles X and V are congruent so
X & V both have a value of 79°
Answer 2.) V=79°
What is the Mark the absolute minimum point of the graph
Answers
Answer:
is in the point x = 1, y = -5
Step-by-step explanation:
The absolute minimum of a graph is the point that is the most far below the x-axis.
Such that if we draw a horizontal line parallel to this point, this line should not intersect the graph in another point. It is usually associated with the lowest value of the variable y.
In the graph, we can see that in the extremes we have dots, so the graph does not continue.
Then we can be sure that the absolute minimum is at the bottom of the large curve, that is in the point x = 1, y = -5
A 15% tip on a dinner bill is $3.60. How much is the bill?
Answers
Answer:
5
Step-by-step explanation:
if you add the tip it is 5 dollars
(6x+9)−(7x+1) find the difference
Answers
explanation: it’s in its simplest form because it cannot be factored
Explanation:
(6x+9)-(7x+1)
remove parentheses and change the sign of each term of expression whenever there is a - in front of an expression in parentheses
6x+9-7x-1
collect like terms
-x+9-1
subtract the numbers
-x+8
The expression 17x is equivalent to the expression x 7.
Answers
Answer:
False
Step-by-step explanation:
There is not a one in the 2 expression listed
If it takes 3 gallons of gas to travel 90 miles, how many gallons of gas does it take to travel 240 miles?
Answers
Answer:
8 gallons
Step-by-step explanation:
Can someone help me with number 4
Answers
Answer:59
Step-by-step explanation:
what is 333x2+999-999 divided by 2 =
Answers
Answer:
333×2+999-999÷2= 333
Step-by-step explanation:
Answer:
333
Step-by-step explanation:
333 x 2 = 666
666 divided by 2 = 333
999 - 999 = 0, so it doesn't do anything to the final number
The answer is 333
hope this helped~
CAN YOU PLEASE HELP ME ?
Answers
Answer:
Where is the question we can help you with
Which number is irrational?
Answers
Answer:
The square root of 3
Step-by-step explanation:
c last answer
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
It cannot be written as a fraction.
Hope this helped, make sure to make this brainiest, thank you.
A company that makes hair products had 9000 people try new shampoo of the 9000 people 72 had a mild allergic reaction what percent of the people had a mild allergic reaction
Answers
Answer:
0.8%
Step-by-step explanation:
Number of people had mild allergic attack = 72
% of people who had mild allergic attack = 72/9000 × 100%
= 0.8%(Answer)
Mike paid $300 to join a gym, for one year, including a membership fee of $60. What is the monthly cost? Write
and solve an equation. Let m represent the monthly cost.
Answers
Answer:
720
Step-by-step explanation:
60×12=720 so the monthly yearly coast would be 720
Find the slope of the line through (9, 4) and (0, 5).
Answers
Answer:
It's just y2-y1 over x2-x1
Step-by-step explanation:
so pick a coordinate and make it 1 and make the other one 2 and put in the numbers.
The slope of the line will be m = -1/9.
What is the general equation of a Straight line?The general equation of a straight line is -y = mx + c
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis
Other possible equations of line are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have a line through (9, 4) and (0, 5).
The slope of the line will be -
[m] = (4 - 5)/(9 - 0)
[m] = - 1/9
Therefore, the slope of the line will be m = -1/9.
To solve more questions on straight line, visit the link below-
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if you answer some of them ill appreciate it ( you don't have to answer all of them )
Answers
Answer:
1) 23, 3, 13
2) 7, 13, 18
3) 9, 6, 77
4) 39, 8, 46
5) 13, 1, 32
6) 45, 9, 54
7) 14, 45, 30
8) 25, 10, 39
Step-by-step explanation:
Left to Right
(3x+15) (2x)
Help pls
Answers
Answer:
(
3
+
1
5
)
(
2
)
(3x+15)(2x)
(3x+15)(2x)
Simplify
1
Distribute
(
3
+
1
5
)
(
2
)
3
(
2
)
+
1
5
(
2
)
Solution
3
(
2
)
+
1
5
(
2
)
Step-by-step explanation:
Answer:
[tex]3x+15+2x=180\\5x=165\\x=33\\[/tex]
Fellow brains pls help.... Is this true or false?
Answers
Y=x anything means True
how do you do this equation ?
solving inequalities
8 ≤ 2x < x + 7
Answers
Answer:
4≤x<7
x€[4,7)
Step-by-step explanation:
8≤2x<x+7
=>8≤2x
=>2x<x+7
x≥4
x<7
therefore
4≤x<7
x€[4,7)
what is the quotient 5 divided by 30
Answers
Answer: 6
Step-by-step explanation:
30÷5=6
Need help with this math problem
Answers
So it’s D= -5y^2
Pls pls help I don’t have time HELP ASAP. It also detects if it’s right or wrong.
Answers
Answer:
noice
Step-by-step explanation:
becuase o=boice
what is 5.3635 rounded to the nearest thousandth
Answers
Answer:
5.364
Step-by-step explanation:
5.3635 is the given number, and because the number next to the thousandths is a five, the number in the thousandths place can be rounded to 4.