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
olya-2409 [2.1K]
2 years ago
6

What is the vertex form of the quadratic equation represented on the table?

Mathematics
1 answer:
sergeinik [125]2 years ago
7 0

Check the picture below, so the parabola looks more or less like so, hmmm with a vertex at (-1 , -4), so, using those values from the table

~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\stackrel{vertex}{\stackrel{h}{-1}~~,~~\stackrel{k}{-4}}\qquad \implies y=a[x-(-1)]^2-4\implies y=a(x+1)^2-4 \\\\\\ \textit{we also know that} \begin{cases} x=2\\ y=14 \end{cases}\implies 14=a(2+1)^2-4\implies 18=9a \\\\\\ \cfrac{18}{9}=a\implies 2=a~\hspace{10em}\boxed{y=2(x+1)^2-4}

You might be interested in
In ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45. What is the value of the cosine of ∠X to the nearest hundredth?
kotegsom [21]

The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

Step-by-step explanation:

The given is,

                   In ΔWXY, ∠Y=90°

                        XW = 53

                         YX = 28

                        WY = 45

Step:1

             Ref the attachment,

             Given triangle XWY is right angled triangle.

             Trigonometric ratio's,

                              Cos ∅  = \frac{Adj}{Hyp}    

             For the given attachment, the trigonometric ratio becomes,

                              Cos ∅  = \frac{XY}{XW}.....................................(1)

             Let, ∠X = ∅

             Where, XY = 28

                         XW =  53

             Equation (1) becomes,

                                 Cos ∅  = \frac{28}{53}

                                 Cos ∅ = 0.5283

                                        ∅ = cos^{-1} (0.5283)

                                        ∅ = 58.109°

Result:

          The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

             

4 0
3 years ago
One plane can travel 30 miles per hour faster than another. one of them goes 185 miles in the same time it takes the other to go
ycow [4]
Plane #1 speed:  x mph
Plane #2 speed:  (x+30) mph

time = time becomes

170 mi        185 mi
---------- = --------------
      x             x+30

Solving for x, the speed of the slower plane, we get

170x + 5100 = 185 x
                                           5100
Then 15x = 5100, and x = ---------- (mi/hr) = 340 mph
                                              15

The slower plane flies at 340 mph, and the faster one at 370 mph.
6 0
3 years ago
Solve 4x + 5 = x + 26​
prohojiy [21]

Answer:

Step-by-step explanation: 7

Subtract 5 on both sides to get 4x = x + 21

then, subtract x from 4x and x is 1, so 3x = 21 then divide by 3 on both sides

8 0
3 years ago
Read 2 more answers
How to find the radius of a sphere when you have the volume given to you
nignag [31]
V=4/3πr^3, so substitute what you know. Input the volume so you only have to solve one variable, the r, radius.
5 0
3 years ago
Generate two equivalent fractions for each fraction. Use fraction tiles or number lines.
oksano4ka [1.4K]
Remember that finding common denominators is only one of the strategies for comparing fractions
5 0
3 years ago
Other questions:
  • Round 1,844,938 to the nearest 1,000 and 100,000
    9·2 answers
  • Serena is cycling from a dance class to her home the equation shows Serena’s distance (y) in miles from her home after x minutes
    8·1 answer
  • How I get x for number 7
    8·1 answer
  • a 28 foot ladder leaning against a building forms a 15 degree angle with the side of the building. how y’all is the building?
    14·1 answer
  • the graph shows the first five terms in a geometric sequence what is the iterative rule for the sequence​
    8·1 answer
  • Ben is making math manipulatives to sell. he wants to ay least sell $450. each manipulative costs $18 to make. he is selling the
    13·2 answers
  • What is the answer for 4/8-2/5
    11·1 answer
  • Which is not a pair of congruent angles in the diagram?
    5·2 answers
  • Help plsssssssssssssss
    13·2 answers
  • 2. Un auto viaja a 60 km/h y se detiene a los 2 segundos. qué distancia recorrió en el
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!