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
AfilCa [17]
2 years ago
10

(a). Consider the parabolic function f(x) = ax² +bx+c, where a ±0, b and care constants. For what values of a, band c is f

Mathematics
1 answer:
ki77a [65]2 years ago
5 0

Information about concavity is contained in the second derivative of a function. Given f(x) = ax² + bx + c, we have

f'(x) = 2ax + b

and

f''(x) = 2a

Concavity changes at a function's inflection points, which can occur wherever the second derivative is zero or undefined. In this case, since a ≠ 0, the function's concavity is uniform over its entire domain.

(i) f is concave up when f'' > 0, which occurs when a > 0.

(ii) f is concave down when f'' < 0, and this is the case if a < 0.

In Mathematica, define f by entering

f[x_] := a*x^2 + b*x + c

Then solve for intervals over which the second derivative is positive or negative, respectively, using

Reduce[f''[x] > 0, x]

Reduce[f''[x] < 0, x]

You might be interested in
Which slope passes through the points (-1,10) and (5,2)
Arisa [49]
-4/3 is the answer to your question
6 0
3 years ago
I need help, can you please help me?
Brums [2.3K]

Answer:

Y= 2/4x + -3

Step-by-step explanation:

6 0
2 years ago
Nick wrote the function p(x) = 17 + 42x – 7x2 in vertex form. His work is below.
Finger [1]

Answer:

step 3

Step-by-step explanation:

he should have subtracted 9 to the outside.

whatever you do to the inside you must do to the opposite to the outside

so your final form must be -7(x-3)^2 + 8

8 0
2 years ago
Determine whether the representation is proportional.y= -9x
valina [46]

Answer:

Yes it is

Step-by-step explanation:

y=-9x means that for every x value, the y value decreases by 9, so it is proportional because the value of y decreases the same amount each time. For example, if x=1, y=-9. If x=5, y=-45, and so on.

4 0
3 years ago
Read 2 more answers
1. Describe a situation that could be modeled by x≤50
Dimas [21]

There are many ways to answer. The x represents some number. We don't know what the number is, but we know that it must be less than or equal to 50. Put another way, the number can be anything you want as long as it doesn't go past 50. We say that 50 is the so called "ceiling" more or less.

Some examples:

* An elevator can only hold 50 people at maximum. Therefore, x can be any number smaller than 50 or 50 itself. Having 51 or over will be too much.

* You can only work 50 hours for one stretch of some 2 week period. If x is the number of hours you work, then x must be 50 or less as written by x \le 50. So x could be x = 37 as it's less than 50, but x = 62 is not possible.

* For some small ride at a theme park, the seats are designed such that only people 50 inches or less can ride on them. If x is the height of a person in inches, then x \le 50 means something like x = 37 is possible but x = 62 is too high.

8 0
3 years ago
Other questions:
  • InstructionsSearch your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your
    10·1 answer
  • How to do a k over 8 equals 7
    5·1 answer
  • A store is mixing up two types of nuts, peanuts and cashews into a 50 lb barrel. peanuts sell for $4 a pound and cashews sell fo
    8·1 answer
  • Find the equation of the lines through the origin and at right angle to lines x^2-5xy+4y^2​
    14·1 answer
  • Find the area of the figure
    9·1 answer
  • What’s the answer to 10(x-2)-3 (x+3)
    10·1 answer
  • 4 ants are standing on a plane Ant A stands at (1,0) B at (0,1) C(-1,0) D at (0,-1) They all start walking to the next ant in al
    9·1 answer
  • Graph the function f(t) = 0.4t.
    10·1 answer
  • 12/4 = 12 1/4 True or False
    13·1 answer
  • PLEASE ANSWER THIS QUESTION PLZ PLZZZZZZZZZ
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!