SOLUTION: find the maximum (or minimum) of each function, also determine the x-intercepts of each function (if any). Express your final answers as a decimal number (rounded to 4 decimal plac

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Question 55410: find the maximum (or minimum) of each function, also determine the x-intercepts of each function (if any). Express your final answers as a decimal number (rounded to 4 decimal places if necessary)
a. f(x)= x2-2x-3
(this is what i came up with so far)
a=1
b=-2 h= -b/2a= 2/2= 1
c=-3
I don't think this is right i need your help!!
b. F(x)= -x2+2x+3
a=1
b=3 h=-b/2a= -(-2)/2(-1)=1
c=3
same thing here...I'm not sure what to do here...
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website!
find the maximum (or minimum) of each function, also determine the x-intercepts of each function (if any). Express your final answers as a decimal number (rounded to 4 decimal places if necessary)
a. f(x)= x^2-2x-3
a=1 (Because a is positive the parabola is a u shape and it's vertex is a minimum.
b=-2
c=-3
To find the vertex:
x= -b/2a= 2/2= 1 Plug this value in to find the height:
f(1)=(1)^2-2(1)-3
f(1)=1-2-3=-4
The minimum value is at the point (1,-4)
The x-intercepts happen when f(x)=0
0=x^2-2x-3 Factor.
0=(x___)(x____)
Two numbers that multiply to give you -3 (c) but add together to give you -2 (b) are: -3 and +1
0=(x-3)(x+1) Use the zero product property and set each parenthesis = 0 and solve for x.
x-3=0 and x+1=0
x=3 and x=-1
The x intercepts are (-1,0) and (3,0).

b. F(x)= -x2+2x+3
a=-1 a is negative so the parabola is n shaped and its vertex is it's maximun point.
b=2
c=3
To find the vertex:
x=-b/2a= -(2)/2(-1)=1
F(1)=-(1)^2+2(1)+3
F(1)=-1+2+3=4
The maximum point is at the vertex:(1,4)
The x-intercepts happen when y=0
0=-x^2+2x+3
-(0)=-(-x^2+2x+3)
0=x^2-2x-3 The same as the first parabola so it's x intercepts are also:(-1,0) and (3,0).

Together they look like this:

Happy Calculating!!!