SOLUTION: I need some help on the following, any help would be appreciated. Finding the intersection of a line and a Parabola A certain pump has a characteristic curve described by the

Question 970145: I need some help on the following, any help would be appreciated.
Finding the intersection of a line and a Parabola
A certain pump has a characteristic curve described by the right half of a parabola described by the equation
h(c) = -0.0025.q^2 + 25
NOTE: The c hangs low but wasn't sure how to type that out so I put it in parenthesis
where the vertical coordinate, h, is in units of feet, and the horizontal coordinate, q, the flow rate, is in gallons per minute.
a) In physics terms, what is maximum height of water that can be supported by this pump with zero flow rate? In mathematical terms, what is the value of h(c) when q = 0?
b) At what value of q will the value of h(c) = 0?
-Shun

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!

The graph shows part of the parabola.
When q=0, h(c)=25.
0=-0.0025q^2 +25
-25=-00025q^2
25=0.0025 q^2
Take positive square root
5=.05 q
q=100
At q=100; q^2=10000; h(c)=0
The vertex is at (0,25)
I am not sure if this answers the full question, but the graph gives an idea of what is occurring.
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