remember, for [tex]y=ax^2+bx+c[/tex] the x value of the vertex is [tex]\frac{-b}{2a}[/tex]
so
given
x value of vertex is -5
and
[tex]y=ax^2-10x+c[/tex]
[tex]\frac{-b}{2a}=\frac{-(-10)}{2a}=\frac{10}{2a}=[/tex]
[tex]\frac{5}{a}=-5[/tex]
multiply both sides by a
5=-5a
divvide both sides by -5
-1=a
a=-1
[tex]y=-1x^2-10x+c[/tex]
comlete the square
remember if we do
[tex]y=a(x-h)^2+k[/tex] (h,k) is the vertex
I know, we can subsitute the known values of te vertex
-5 for h and 20 for k then expand
[tex]y=-1(x-(-5))^2+20[/tex]
[tex]y=-1(x+5)^2+20[/tex]
[tex]y=-1(x^2+10x+25)+20[/tex]
[tex]y=-1x^2-10x-25+20[/tex]
[tex]y=-1x^2-10x-5[/tex]
a=-1
c=-5
