# 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
Mar 29, 2016

Answer is:

${x}_{s y m m} = 2$

#### Explanation:

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

${x}_{s y m m} = - \frac{b}{2 a} = - \frac{- 4}{2 \cdot 1} = 2$

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 $\overline{x}$ of the two roots:

$\overline{x} = \frac{{x}_{1} + {x}_{2}}{2}$

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

$\overline{x} = \frac{- 2 \frac{b}{2 a}}{2}$

$\overline{x} = \frac{- \cancel{2} \frac{b}{2 a}}{\cancel{2}}$

$\overline{x} = - \frac{b}{2 a}$