#"given the equation of a parabola in standard form
"#
#•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0#
#"then the x-coordinate of the vertex is"#
#•color(white)(x)x_(color(red)"vertex")=-b/(2a)#
#f(x)=-x^2-3x-6" is in standard form"#
#"with "a=-1,b=-3,c=-6#
#rArrx_(color(red)"vertex")=-(-3)/(-2)=-3/2#
#"substitute this value into f(x) for y-coordinate"#
#rArry_(color(red)"vertex")=-(-3/2)^2-3(-3/2)-6=-15/4#
#rArrcolor(magenta)"vertex"=(-3/2,-15/4)#
#color(blue)"Intercepts"#
#• " let x = 0, in equation for y-intercept"#
#• " let y = 0, in equation for x-intercepts"#
#x=0toy=-6larrcolor(red)" y-intercept"#
#y=0to-x^2-3x-6=0#
#"checking the value of the "color(blue)"discriminant"#
#Delta=b^2-4ac=(-3)^2-(4xx-1xx-6)=-15#
#"since "Delta<0" then no real solutions"#
#rArrf(x)" does not intersect with the x-axis"#
graph{-x^2-3x-6 [-10, 10, -5, 5]}
