SOLUTION: Hi, This is what my book says for the four problems I need help on: For each of the following functions, reason with the symbolic forms to find all x for which f(x)=0. Then s

Question 258558: Hi,
This is what my book says for the four problems I need help on:
For each of the following functions, reason with the symbolic forms to find all x for which f(x)=0. Then sketch a graph and find the minimum or maximum value of the function.
1. d(x)=(2x-5)(x+4)
2. f(x)=x^2+5x-6
3. g(x)=x^2-12x
4. h(x)=-x^2+7x+18
I think I would be fine sketching the graph. But I'm just not too sure on how to get to that point.
Thank you very much for your help.
K.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Lets take each one separately:
1. d(x)=(2x-5)(x+4)
set d(x) = 0 to get
(2x-5)(x+4) = 0
set each parenthesis = 0 and solve for x to get
(2x-5)=0
2x=5
x = 5/2
and then
x+4=0
x=-4
The minimum occurs at (-3/4, -21.125)
graph is

--
2. f(x)=x^2+5x-6
factoring, we get
(x+6)(x-1)
Set f(x) = 0 to get
(x+6)(x-1) = 0
Set each parenthesis = 0 and solve for x to get
(x+6)=0
x = -6
and then
x-1=0
x=1
The minimum occurs at (-5/2, 12.75)
graph is

--
3. g(x)=x^2-12x
factoring, we get
(x)(x-12)
Set f(x) = 0 to get
(x)(x-12) = 0
Set each parenthesis = 0 and solve for x to get
x=0
and then
x-12=0
x=12
The minimum occurs at (6, -36)
graph is

--
4. h(x)=-x^2+7x+18
factoring, we get
-1(x+2)(x-9)
Set f(x) = 0 to get
(x+2)(x-9) = 0
Set each parenthesis = 0 and solve for x to get
x+2=0
x = -2
and then
x-9=0
x=9
The maximum occurs at (7/2, 30.25)
graph is

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