Question 965766: Can someone please explain how i work this out? im finding it very difficult to understand.
The size of a colony of rare termites is related to the size of the colony’s
mound. The relationship can be modeled using the equation below:
ℎ = −N^2 + 25N − 5
Where N is thousands of termites and ℎ is the height of the mound in
centimeters.
Sketch the graph showing the relationship between the number of termites(x-axis)and the height of the mound (y-axis).Show the coordinates of the y-intercept only.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! You can put the equation into standard form to help with graphing, and you can find the h intercept, and the x intercepts.
Standard form would be like,  , with variables h for your function name, N for your independant variable name, "a" a factor, and vertex (r,k). Your function has the vertex as a maximum point. You need to review how to Complete The Square. See the lesson in my profile.
You can find the x-intercepts with  ;
 , the roots or x-intercepts.
Find the h intercept when N=0.
 , the point (0,-5).
Each mark on the vertical scale is 17, for thousands of centimeters of mound height. Each mark horizontally is whole number thousands of termites.
The vertex is very near N=2.5
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