#"given a quadratic equation in standard form"#
#•color(white)(x)y=ax^2+bx+c color(white)(x)a!=0#
#"then the x-coordinate of the vertex which is also"#
#"the axis of symmetry is"#
#•color(white)(x)x_(color(red)"vertex")=-b/(2a)#
#y=-x^2-6x-5" is in standard form"#
#"with "a=-1,b=-6,c=-5#
#rArrx_(color(red)"vertex")=-(-6)/(-2)=-3#
#"substitute this value into y for y-coordinate"#
#rArry_(color(red)"vertex")=-(-3)^2-6(-3)-5=4#
#rArrcolor(magenta)"vertex "=(-3,4)#
#color(blue)"axis of symmetry is "x=-3#
#"to find the x-intercepts let y = 0"#
#rArr-x^2-6x-5=0#
#"multiply through by "-1#
#rArrx^2+6x+5=0#
#"the factors of + 5 which sum to + 6 are + 5 and + 1"#
#rArr(x+5)(x+1)=0#
#"equate each factor to zero and solve for x"#
#x+5=0rArrx=-5#
#x+1=0rArrx=-1#
#rArrx=-5,x=-1larrcolor(red)" x-intercepts"#
graph{(y+x^2+6x+5)(y-1000x-3000)((x+3)^2+(y-4)^2-0.04)=0 [-10, 10, -5, 5]}
