Answer:
Step-by-step explanation:
f (x) = a(x - h)^2 + k
1.)When finding the vertex, you have to know that vertex (h (or -x),k) and
so if h=1, that means that -x=1 and k=8
so Vertex is (-1,8)
2.) The "a" is -2 so that means that the graph is going down and usually when you want to find your points in the graph, you must do the same principles as you would for slope (only works on he first two points, and after that the slope changes as the parabola goes down)
So First slope is (-2/1 = -2) so going down 2 and going right or left will lead to points (2,6) and (0,6).
3.) You must find your zeros by using Algebra and factoring to find the zeros
(factor)
[tex]-2(x-1)^{2} +8=0\\-2(x^{2} -2x+1) +8= 0\\-2x^{2} +4x+6=0[/tex]
(Solve)
[tex]-2(-x^{2} +2x+3)=0\\-2(-x+3)(x+1)=0\\\\Must \\Divivde\\2 \\expressions\\Apart\\to\\ solve\\for\\ roots\\[/tex]
[tex]expression 1\\2(-x+3)=0\\-2x+6=0\\-2x=-6\\x=3\\(3,0)[/tex]
[tex]expression 2\\(x+1)=0\\x=-1\\(-1,0)[/tex]
