Question

can someone help me find the maximum value for f(x) = -x^2 - 2 x + 24.

here is what I found so far: the parabola has a y intercept at (0,24) and 2 intercepts that occur at -6 and 4

Answer 1

You want to find the vertex. Do you know how to do this?

Answer 2

the maximum value of an upside down parabola; is the vertex

Answer 3

or the derivative depending on what class your in :)

Answer 4

the vertex cordinates are ( -1, and ?)

Answer 5

plug in x=-1 and solve for y

Answer 6

i didnt find the other one

Answer 7

plug into the original function?

Answer 8

yes: y= (.....)

Answer 9

what does y= when x=-1? well, we use the equation to determine that :)

Answer 10

Yes the vertex is at:
\[\huge (\frac{-b}{2a},f(\frac{-b}{2a}))\]
when the function is written as ax^2+bx+c

Answer 11

or we can maipulat eit into a vertex form ...

Answer 12

manipulate even ....

Answer 13

yes, but you'd have to complete the square. easier in its current form :)

Answer 14

well this one is actually pretty easy

Answer 15

f(x) = -x^2 - 2 x + 24

f(x) = -(x^2 + 2 x +1) -1 + 24

f(x) = -(x+1)^2 +23

right?

Answer 16

ok i found y=27 when x=-1

Answer 17

lets chk that then :)

f(-1) = -(-1)^2 - 2(-1) + 24
= -1 +2 + 24
= 25

might be better

Answer 18

ok so (
-1,25) are my vertex

Answer 19

i pulled out a -1 in my vertex form instead of the proper +1 ....

f(x) = -(x+1)^2 + 25

would have been gooer

Answer 20

yes, and the vertex tells us the "highest" point in this case

Answer 21

so the highest point is the min and the lowest point is the max

Answer 22

let me draw it

Answer 23

the vertex point is our highest point on this f(x) so the highest value we get is: 25

Answer 24

Yes, when the coefficient of x^2 is negative, the parabola opens down and has a maximum at the vertex; when it's positive, the parabola opens up and has a minimum at the vertex

Answer 25

so the maxis 25?

Answer 26

yes:25

Answer 27

unless we found a different meaing for maximum and 25 ... id would say that yes; the maximum is 25

Answer 28

so find the vertex's then plug it back into the function to find the minimum and maximum?

Answer 29

what would minimum suggest to you? smallest possible value right?

Answer 30

yes

Answer 31

the minimum of this function is then: -infinity

Answer 32

yes so it would be concave up

Answer 33

cave down