First,
We are dealing with parabola since the equation has a form of,
[tex]y=ax^2+bx+c[/tex]
Here the vertex of an up - down facing parabola has a form of,
[tex]x_v=-\dfrac{b}{2a}[/tex]
The parameters we have are,
[tex]a=-5,b=-10, c=6[/tex]
Plug them in vertex formula,
[tex]x_v=-\dfrac{-10}{2(-5)}=-1[/tex]
Plug in the [tex]x_v[/tex] into the equation,
[tex]y_v=-5(-1)^2-10(-1)+6=11[/tex]
We now got a point parabola vertex with coordinates,
[tex](x_v, y_v)\Longrightarrow(-1,11)[/tex]
From here we emerge two rules:
- If [tex]a<0[/tex] then vertex is max value
- If [tex]a>0[/tex] then vertex is min value
So our vertex is minimum value since,
[tex]a=-5\Longleftrightarrow a<0[/tex]
Hope this helps.
r3t40
