Step-by-step explanation:
a) In order to find the maximum value of [tex]f(x)=-x^2+4x-3[/tex] we must find the vertex of the parabola. Using the equation [tex]x=\frac{-b}{2a}[/tex] we can find the x coordinate of the vertex.
This would mean that
[tex]x=\frac{-4}{-2} \\\\x=2[/tex]
Now we can plug 2 into [tex]f(x)=-x^2+4x-3[/tex] in order to find the y- value
[tex]f(2)=-2^2+4(2)-3\\\\f(2)=-4+8-3\\f(2)=1[/tex]
This means that the maximum value of [tex]f(x)=-x^2+4x-3[/tex] is at the point (2,1)
For g(x) we can look at the graph and see where the vertex is as that will be the maximum value. When we look at the graph we can see that it is approximately (-2,3.8)
b) Now that we know the values for each of the functions, we can compare them. Function g has the greater maximum value as [tex]3.8\geq 1[/tex]
