Here i how I would do it:f(x)=−x2+8x+15
set f(x) = 0 to find the points at which the graph crosses the x-axis. So−x2+8x+15=0
multiply through by -1x2−8x−15=0
(x−4)2−31=0
x=4±31−−√
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through(0,15),(4−31−−√,0)and(4+31−−√,0)
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:f(x)=31−(x−4)2
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.
