"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]}
