Start by setting the function equal to 0 and then moving the -5.4 over to the other side of the equals sign. [tex]-.2 x^{2} -2.8x=5.4[/tex]. The first rule for completing the square is that the leading coefficient be a +1. Ours is a -.2. So we need to factor it out. [tex]-.2( x^{2} +14x)=5.4[/tex]. Now we will take half the linear term, square it, and add it to both sides. Our linear term is 14. Half of 14 is 7, and 7 squared is 49. So we add 49 in to the left side just fine, but we cannot forget about that -.2 hanging around out front as a multiplier. What we have actually "added" in is -.2*49 which is -9.8. Now here's what we have after all that: [tex]-.2( x^{2} +14x+49)=5.4-9.8[/tex]. In that process, we have created a perfect square binomial on the left. Along with expressing that binomial we will do the math on the right: [tex]-.2(x+7) ^{2} =-4.4[/tex]. Now we will move the -4.4 back over by addition, and it will then be apparent as to what our vertex is. The y coordinate of the vertex will give us the max height of the water. [tex]-.2(x+7) +4.4=y[/tex]. As you can see, our work matches choice C from above.
