SOLUTION: Y(x)=-x2+17x-34 I need to know the value of x when y is at maximum value? What is the maximum value of y? Since negative y values are impossible for operating the MRI machine, w

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Question 46106: Y(x)=-x2+17x-34 I need to know the value of x when y is at maximum value? What is the maximum value of y? Since negative y values are impossible for operating the MRI machine, what is the range of x values for y to be greater than or equal to zero? What is te range of x values where y is at 90% of its maximum value? Plot a graph showing all of the above information.
Answer by Nate(3500)   (Show Source): You can put this solution on YOUR website!
Y(x) = -x^2 + 17x - 34
I need to know the value of x when y is at maximum value?
v(-b/2a,f(x))
v(8.5,38.25) the vertex is the maximum point
Since negative y values are impossible for operating the MRI machine, what is the range of x values for y to be greater than or equal to zero?








What is the range of x values where y is at 90% of its maximum value?



Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=15.3 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6.54423927843921, 10.4557607215608. Here's your graph:
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