The average of the roots of the quadratic formula = -b/2a, assuming the discriminant0, explain why h=-b/2a where V (h,k) is the vertex of this parabola.

Question

The average of the roots of the quadratic formula = -b/2a, assuming the discriminant>0, explain why h=-b/2a where V (h,k) is the vertex of this parabola.

anonymous · Answer

$$y=ax^2+bx+c$$
$$y=a(x^2+\frac{b}{a}x)+c$$
$$y=a(x+\frac{b}{2a})^2+k$$ so vertex is at 
$$(-\frac{b}{2a},k)$$

savvy · Answer

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parabola is symmetric about its axis....hence just midway between both the roots lies the vertex....
so, midway is (x1 + x2)/2
and x1 + x2 is -b/a [sum of roots]
so vertex is at -b/2a

anonymous · Answer

Just curious what is the discriminant is = 0

anonymous · Answer

if the discriminant is zero it means
1) you have a prefect square, like $y=(x+3)^2$ and 
2) there is only one zero, namely at the vertex