Originally Posted by
Quacky y=-4x^2-9x-2
Ok, the line will cut the y axis where x=0.
Substitute x=0 into the equation, and you get y=-2. So point of interception is at:
(0,-2)
Now, the line will cut the x axis where y=0. To find this, we can try to factorise:
-4x^2-9x-2=0
4x^2+9x+2=0
(4x+1)(x+2)=0
x=-2 and x=-1/4
x intercepts are
$\displaystyle (-2,0)$ and $\displaystyle (-1/4,0)$
Parabolas are symmetrical, so if you take the x intercepts, the line of symmetry will be halfway between them.
$\displaystyle -2.25/2 = -1.125$ (wow, nasty numbers)
x=-1.125 is the line of symmetry.
A question about the vertex: Have you covered differentiation?