How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #F(x)=x^2- 4x -5#?

1 Answer
Costas C.
Mar 29, 2016

Answer is:

#x_(symm)=2#

Explanation:

The value of the axis of symmetry in a quadratic polynomial function is:

#x_(symm)=-b/(2a)=-(-4)/(2*1)=2#

Proof

The axis of symmetry in a quadratic polynomial function is between the two roots #x_1# and #x_2#. Therefore, ignoring the y plane, the x value between the two roots is the average #bar(x)# of the two roots:

#bar(x)=(x_1+x_2)/2#

#bar(x)=((-b+sqrt(Δ))/(2a)+(-b-sqrt(Δ))/(2a))/2#

#bar(x)=(-b/(2a)-b/(2a)+sqrt(Δ)/(2a)-sqrt(Δ)/(2a))/2#

#bar(x)=(-2b/(2a)+cancel(sqrt(Δ)/(2a))-cancel(sqrt(Δ)/(2a)))/2#

#bar(x)=(-2b/(2a))/2#

#bar(x)=(-cancel(2)b/(2a))/cancel(2)#

#bar(x)=-b/(2a)#

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