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
dolphi86 [110]
3 years ago
5

If the maximum value of y =-x²+ax+b is 8 when x = 3, find the values of a and b​

Mathematics
1 answer:
anzhelika [568]3 years ago
5 0

Answer:

a = 6 and b = -1.

Step-by-step explanation:

To find the maximum value of y = -x²+ ax + b we differentiate it with respect to x to find the value of x at which it is maximum.

So dy/dx = d(-x²+ ax + b)/dx = -2x + a

we equate it to zero.

-2x + a = 0

-2x = -a

a = 2x

Now, given that x = 3 at the maximum value,

a = 2x = 2(3) = 6

Also, substituting y = 8 and x = 3 into y, we have

y = -x²+ ax + b

8 = -(3)²+ a(3) + b

8 = -9 + 3a + b

3a + b = 8 + 9

3a + b = 17

So, b = 17 - 3a

substituting a = 6, we have

b = 17 - 3(6)

b = 17 - 18

b = -1

So, a = 6 and b = -1.

You might be interested in
How to isolate scalars from a matrix
I am Lyosha [343]
The technique of matrix isolation involves condensing the substance to be studied with a large excess of inert gas (usually argon or nitrogen) at low temperature to form a rigid solid (the matrix). The early development of matrix isolation spectroscopy was directed primarily to the study of unstable molecules and free radicals. The ability to stabilise reactive species by trapping them in a rigid cage, thus inhibiting intermolecular interaction, is an important feature of matrix isolation. The low temperatures (typically 4-20K) also prevent the occurrence of any process with an activation energy of more than a few kJ mol-1. Apart from the stabilisation of reactive species, matrix isolation affords a number of advantages over more conventional spectroscopic techniques. The isolation of monomelic solute molecules in an inert environment reduces intermolecular interactions, resulting in a sharpening of the solute absorption compared with other condensed phases. The effect is, of course, particularly dramatic for substances that engage in hydrogen bonding. Although the technique was developed to inhibit intermolecular interactions, it has also proved of great value in studying these interactions in molecular complexes formed in matrices at higher concentrations than those required for true isolation.
3 0
3 years ago
100 points and brain list giving Help ASAP
sergij07 [2.7K]

-4x+60\geq84\qquad\text{subtract 60 from both sides}\\\\-4x\geq24\qquad\text{change the signs}\\\\4x\leq-24\qquad\text{divide both sides by 4}\\\\x\leq-6\to x\in(-\infty,\ -6]\\\\x-3

6 0
3 years ago
Use the graph to answer the question. About how many more website hits were there on Tuesday than on Monday? A. 700 B. 400 C. 60
nadezda [96]
In this graph, each day has its own graph, starting at the bottom with Monday, to the top at Sunday. To know how many hits each day had, go to the end of the graph, and the closest number at the bottom is how many hits there were. This graph states that there were around 1900 hits on Tuesday, and 1300 on Monday. To get the answer we then take the difference, getting 600.
5 0
3 years ago
-4 + 8 - 5
pochemuha

Answer:

-1

Step-by-step explanation:

read warriors

by eren hunter.

5 0
1 year ago
Read 2 more answers
The double number line shows that 1 game of bowling 14 dollars what table represents the cost per game of bowling?
nikitadnepr [17]

Answer:

The second one is correct!

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is a real-world situation that can be modeled by the equation | x - 14 | = 3?
    13·1 answer
  • What is the second term of the sequence generated by the formula an = 3n?
    7·2 answers
  • Find the first four terms of the sequence given a1=18 and an+1=2+an2. A. 18, 10, 6, 5 B. 18, 10, 6, 9 C. 18, 14, 6, 9 D. 18, 10,
    10·1 answer
  • The question: how old am I if 400 reduced by 2 times my age is 352?
    8·1 answer
  • What is -7.08 as a fraction
    8·2 answers
  • The perimeter of a square is represented by 20n-8. Write an expression that will represent each side of the square.
    14·2 answers
  • Select all the expressions that are equivalent to 4 − x.
    13·2 answers
  • SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU Brainly!!!!! ONLY IF ITS RIGHT
    6·1 answer
  • help At 1:00 P.M. the water level of a pool is 13 inches At 1:30 P.M. the water level is 18 inches At 2:30 the water level is 28
    6·1 answer
  • Help pleaseeeeeeeeeeeee
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!