SOLUTION: I need help with this problem: Determine the parameter k so that the quadratic equation k x^2-16x+16=0 had exactly one real solution. A world problem is related to this probl

Question 454646: I need help with this problem:
Determine the parameter k so that the quadratic equation k x^2-16x+16=0 had exactly one real solution.
A world problem is related to this problem too: An object is tossed into the air with an upward velocity of 22 feet per second from the top of a 10-foot wall. Its flight is governed by h(t)=16t^2-22t-10=0. What is the time for the object to reach the highest point, and what is the altitude of this highest point?

Thank you very much.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Determine the parameter k so that the quadratic equation k x^2-16x+16=0 had exactly one real solution.
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From the quadratic formula the zeros are:

In order for there to be only one real zero, the discriminant
must equal zero.
In this case, a = k, so we have
16^2 - 4*k*16 = 0
16 = 4k
This gives k = 4
As a check, we plot the graph, and confirm that the vertex lies on the x-axis:

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