SOLUTION: Ihave three problems that my father brought to my attention. H etried to do them and could not figure them out. I for the life of me can't either. Hetold me someone said they some

Question 160957: Ihave three problems that my father brought to my attention. H etried to do them and could not figure them out. I for the life of me can't either. Hetold me someone said they some sort of algebra called grinding.Can someone help? Question is: Write the minimum or maximum point for each function,and give the coordinates for that point. 1. y=x^2-4x+1 hint start at 0 and increase. 2. y=x^2-8x-5 hint start at 2 and increase. 3. y=-2^2+2x+6 hint start at -1 and increase. Can anyone help us with these.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
I think the procedure is just start at a point get a value for the function, move over get another point, etc. until you see the pattern that the function has either maxed out (reached a maximum) or bottomed out (reached a minimum). Plug and chug we used to call it.
.
.
.
a)
y=x^2-4x+1
y(0)=0-0+1=1
y(1)=1-4+1=-2
y(2)=4-8+1=-3
y(3)=9-12+1=-2
Looks like (2,-3) is the minimum.

.
.
.
b)
y=x^2-8x-5
y(2)=4-16-5=-17
y(3)=9-24-5=-20
y(4)=16-32-5=-21
y(5)=25-40-5=-20
Looks like (4,-21) is the minimum.

.
.
.
c)
y=-2x^2+2x+6
y(-1)=-2-2+6=2
y(0)=0+0+6=6
y(1)=-2+2+6=6
y(2)=-8+4+6=2
The maximum is between 0 and 1, at x=1/2.
y(1/2)=-1/2+1+6=6.5
(0.5,6.5)

.
.
.
Just a hint, for quadratic equations in the form , the max or min always occurs at

so if we look at your examples again,
y=x^2-4x+1, a=1, b=-4,
y=x^2-8x-5, a=1, b=-8,
y=-2x^2+2x+6, a=-2, b=2,
Same answers just much faster than guessing.
RELATED QUESTIONS
Quadratic equations are not my strong suit and I recently failed a quiz based on them. My (answered by richard1234)

Okay, only four problems left for my homework assignment and I cannot figure them out (go (answered by nycsharkman)

Okay, only four problems left for my homework assignment and I cannot figure them out (go (answered by Earlsdon)

translate this to predicate calculus: Many, many years ago when I was twenty-three I... (answered by longjonsilver)

Hello I have a lot of math to do for homework and I forgot how to do it since we just... (answered by josgarithmetic)

While trying to figure these problems out i ran into trouble with finding the final... (answered by Alan3354)

I have Three problems on my work sheet that I do not understand how to do. The... (answered by ankor@dixie-net.com)

x/5 - y/10 = 4 x/2 + y/4 = 5 Solve the system of equation using the addition... (answered by Edwin McCravy)

For f(x)=((x^3-2x)/(x+1)) find f(x+h) My work: The only solution I have been able to... (answered by josgarithmetic)