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
vlabodo [156]
3 years ago
12

a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the

equation of the parabola.
Mathematics
1 answer:
nlexa [21]3 years ago
7 0

Answer:

The standard equation of the parabola is:

y=-\frac{3}{2}x^2+12x-18

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}

Then the equation of the parabola becomes:

y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18

You might be interested in
Which of the following lengths can be the sides of a triangle?
Dmitriy789 [7]

Answer:

C. 44 cm, 30cm, and 16 cm

Step-by-step explanation:

Sana nakatulong

7 0
3 years ago
A restaurant sells burritos for $8.00 each. To buy supplies, the restaurant pays $1.50 for the meat and $1.00 for the other ingr
3241004551 [841]

Answer:

isnt it just 2.50$ ?

Step-by-step explanation:

1$ + 1.5$ = 2.5$ ?

meat + everything else = total

6 0
3 years ago
Read 2 more answers
I need a lot of help, I’m really confused on what we are learning currently.
Virty [35]

7m+2=7n−5

Swap sides so that all variable terms are on the left hand side.

7n−5=7m+2

Add 5 to both sides.

7n=7m+2+5

Add 2 and 5 to get 7.

7n=7m+7

Divide both sides by 7.

7

7n

=

7

7m+7

Dividing by 7 undoes the multiplication by 7.

n=

7

7m+7

Divide 7+7m by 7.

n=m+1

3 0
3 years ago
Bailey and Elena compete in a swim race
gogolik [260]

Answer:

yaah then bailey has fun with her

Step-by-step explanation:

5 0
3 years ago
HELPPPP will mark brainliest
ArbitrLikvidat [17]

Answer:

12x-2

Step-by-step explanation:

You need to add 5x+1 and 7x-3.

5x+1+7x-3.

We need to organize this into common terms.

5x+7x+1-3

Now we simplify.

12x-2

That is the final answer!!

Hope this helped!!!! :D

6 0
3 years ago
Other questions:
  • Please explain to me what the Law Of Syllogism is. 100pts... Explain it well please...
    5·2 answers
  • Start time 6:57pm elasped time 47 min
    9·1 answer
  • What are equivalent to 2:9
    5·1 answer
  • ANSWER ASAP
    12·2 answers
  • A scale drawing of a bathroom is shown below:
    15·1 answer
  • Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th
    7·1 answer
  • The double number line below shows the prices for a certain number of jars of peanut butter at a store. Which statement correctl
    15·2 answers
  • Please help me please
    14·1 answer
  • Olivia bought a coat for a trip to Alaska and used a coupon for 20% off the coat price. The total cost of her coat, with the dis
    8·1 answer
  • How can i use the slope formula to find the slope between (2, -7) and (1, 6)
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!