1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ratling [72]
3 years ago
12

Which function does the graph represent?

Mathematics
1 answer:
jeyben [28]3 years ago
7 0

Answer:

The function which represents the graph is:

y=-\left(x\:-\:2\right)^2+\:3

Hence, option  B is correct.

The graph is also attached.

Step-by-step explanation:

From the graph, it is clear that:

The vertex = (2, 3)

The y-intercept = (0, -1)

Let us check the equation

y=-\left(x\:-\:2\right)^2+\:3

Determining the y-intercept:

The value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

substituting x = 0 in teh equation

y=-\left(x\:-\:2\right)^2+\:3

y=-\left(0\:-\:2\right)^2+\:3

y=-2^2+3

y=-4+3

y=-1

Thus,

The point representing the y-intercept is:  (0, -1)

Determining the vertex:

The vertex of an up-down facing parabola of the form ax² + bx + c is:

x_v=-\frac{b}{2a}

As the equation is

y=-\left(x\:-\:2\right)^2+\:3

Rewriting the equation y=-\left(x\:-\:2\right)^2+\:3 in the form ax² + bx + c:

y=-x^2+4x-1

The Parabola params are:

a=-1,\:b=4,\:c=-1

Thus,

x_v=-\frac{b}{2a}

x_v=-\frac{4}{2\left(-1\right)}

x_v=2

Now plug in x_v=2 in the equation to find y_v

y_v=-x^2+4x-1

\:y_v=-\left(2\right)^2+4\left(2\right)-1

y_v=-4+8-1

y_v=3

Therefore, the vertex of the equation is:  (2, 3)

Hence, the function which represents the graph is:

y=-\left(x\:-\:2\right)^2+\:3

Hence, option  B is correct.

The graph is also attached.

You might be interested in
b. From where the shoes spilled (48°N, 161°W) to where they were found on May 22nd 1996 (54°N, 133°W), how many kilometers did t
dsp73

To find kilometers using latitude and longitude:

distlon = lon2 - lon1   = 133-161 = -23

distlat = lat2 - lat1  = 54-48 = 6

a = (sin(distlat/2))^2 + cos(lat1) * cos(lat2) * (sin(distlon/2))^2  

a = (sin(6/2)^2 + cos(48)*cos(54)* sin(-23/2)^2

c = 2 * arctan2( sqroot(a), sqroot(1-a) )  

d = R * c (where R is the radius of the Earth, 6373 km's)

d = 2052 km's

April 30th to May 22nd is 23 days.

23 days x 24 hours per day = 552 hours.

Rate of travel = 2052 / 552 = 3.717 km per hour ( round answer as needed.)

3 0
3 years ago
7over10 subtract 5over12 in simplest form
Andrews [41]

Answer: =\frac{17}{60}\quad \left(\mathrm{Decimal:\quad }\:0.28333\dots \right)

Step-by-step explanation:

\left(\frac{7}{10}\right)-\left(\frac{5}{12}\right)

=\frac{7}{10}-\frac{5}{12}

=\frac{42}{60}-\frac{25}{60}

=\frac{42-25}{60}

=\frac{17}{60}

4 0
2 years ago
Order the values from least to greatest.<br> 8, |3|, -5, |-2|, -2
jok3333 [9.3K]

Step-by-step explanation:

-5 , -2, |-2| ,|3|, 8

the absolute value makes the sign positive no matter what, for example |-2| becomes 2

4 0
3 years ago
A bakery makes 260 donuts in 4 hours. At this rate, how many donuts can they make in 6 hours?
Yuri [45]

Answer:

385

Step-by-step explanation:

260 divided by 4 =65

65 + 65 + 260= 385

7 0
2 years ago
How would I figure out a linear equation with two plot points with fractions? (1/3(6),3) and (1/2(19),-2) are my two plot points
murzikaleks [220]

Answer: m=\frac{-30}{79},\ y=5.40

Step-by-step explanation:

Given

Points are \left(6\frac{1}{3},3\right),\ \left(19\frac{1}{2},-2\right)

Convert mixed numeral to fraction

\left(6\frac{1}{3},3\right)\Rightarrow \left(\dfrac{19}{3},3\right)\\\\\left(19\frac{1}{2},-2\right)\Rightarrow \left(\dfrac{39}{2},-2\right)

Slope of the line is

\Rightarrow m=\dfrac{3-(-2)}{\dfrac{19}{3}-\dfrac{39}{2}}\\\\\Rightarrow m=\dfrac{5}{\dfrac{38-117}{6}}\\\\\Rightarrow m=\dfrac{-30}{79}

Equation of line

\Rightarrow \dfrac{y-3}{x-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow \dfrac{y-3}{0-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\Rightarrow y-3=\dfrac{190}{79}\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40

3 0
2 years ago
Other questions:
  • Find the volume of a cone with base area 36π ft2 and a height equal to twice the radius. Give your answers both in terms of π an
    7·1 answer
  • Solve the equation below <br> 3x—5(x+2)=-40
    11·1 answer
  • A passenger traub keaves a depot 1.5 hours after a freight train leaves the same depot. The passenger train is travleing 18 mph
    14·2 answers
  • A piece of cardboard has been cut into a rectangle with side lengths represented by 9.5x+14.3y cm and 11.7x+22.8y cm. What is th
    6·1 answer
  • the volume of a triangular pyramid is 300 cubic meters. what is the area of the pyramid's base of the pyramid height is 3 meters
    7·1 answer
  • Tonya knows a half a gallon of juice at the store cost $2.29. She decided to to buy 10gallons of juices for a party. how much mo
    10·1 answer
  • X(x+3)(x+3)=0<br><br> solve the equation only one answer
    12·1 answer
  • Evelyn owns a small business selling used books. She knows that in the last week 86 customers paid cash, 30 customers used a deb
    15·1 answer
  • 9. Sam is building a new house. He needs wood spacers that are each
    8·1 answer
  • Awnser this question for 10 points..... 1+9+19,000+1,000,000+60+190+30=
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!