SOLUTION: Hi, the following question I dont know where to start with: it is the daily profit for whitegoods store from sale of bar fridges is given by P(x)= -x^2+40x+825 where x is number o

Question 50513: Hi, the following question I dont know where to start with:
it is the daily profit for whitegoods store from sale of bar fridges is given by P(x)= -x^2+40x+825 where x is number of bar fridges sold. Find the function's vertex and intercepts.
Thanks very much if you could please help me with this one!
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
P(x) = -x^2 + 40x + 825
v(-b/2a,f(x))
-b/2a = -40/(2*-1) = -40/-2 = 20
P(20) = -(20)^2 + 40(20) + 825 = -400 + 800 + 825 = 1,225
v(20,1225)
x-intercepts
0 = -x^2 + 40x + 825
825 = x^2 - 40x
825 + 400 = (x - 20)^2
1225 = (x - 20)^2
+-35 = x - 20
20+-35 = x
(-15,0) and (55,0) are the intercepts

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
P(x)= -x^2+40x+825
Rewrite as follows:
-(x^2-40x+?)= P(x)-825+?
Complete the square to get:
-(x^2-40x+400) = P(x)-825-400
-(x-20)^2 = P(x)-425
This follows the form y-k=(x-h)^2
where (h,k) is the vertex.
For your problem h=20,k=425
Vertex is (20,425).
---------
To find the y-intercept let x=0 in the original equation.
Then P(0)=825.
So, y-intercept is (0,825)
---------
To find the x-intercepts use the quadratic formula.
Cheers,
Stan H.
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