1. the x value of the vertex in form ax^2+bx+c=y is -b/2a so
-2x^2+8x-18 x value of vertex is -8/(2*-2)=-8/-4=2
plug it in to get y value -2(2)^2+8(2)-18 -2(4)+16-18 -8-2 -10
vertex is at (2,-10) or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k) so as follows y=(-2x^2+8x)-18 y=-2(x^2-4x)-18 y=-2(x^2-4x+4-4)-18 y=-2((x-2)^2-4)-18 y=-2(x-2)^2+8-18 y=-2(x-2)^2-10 vertex is (2,-10)
5. vertex is the time where the speed is the highest at about t=10, the speed is at its max
The vertex of the graph is the point where the line crosses its axis of symmetry. The axis of symmetry is the line that you could fold the graph on and it would be symmetrical about that line. In your graph you could fold it on the x=10 line (which is a vertical line (goes up and down)) and the graph would be symmetrical. This is saying that you could technically fold this graph in HALF and it would be 100% symmetrical if you were to fold it on that line. Therefore your vertex is the point on the graph where your line crosses the axis of symmetry which would be (10,something). Looking at your graph it is (10,60). Let me know is you need me to explain further
Well so 15000-2000 leaves 13000kgs of available weight allowed. Then 13000 divided by 1500 we get around 8.67 cubicmeters of gravel to be allowed to be lifted safely.
