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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (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?
0+=+-x%5E2+%2B+17x+-+34
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-17+%2B-+sqrt%28+17%5E2+-+4%2A-1%2A-34+%29%29%2F%282%2A-1%29+
x+=+%28-17+%2B-+sqrt%28+289+-+136+%29%29%2F%28-2%29+
x+=+%28-17+%2B-+3%2Asqrt%28+17+%29%29%2F%28-2%29+
x+=+8.5+%2B-+1.5%2Asqrt%28+17+%29+
8.5+-+1.5%2Asqrt%28+17+%29+%3C=+x+%3C=+8.5+%2B+1.5%2Asqrt%28+17+%29
graph%28600%2C600%2C-4%2C16%2C-4%2C39%2C-x%5E2+%2B+17x+-+34%29
What is the range of x values where y is at 90% of its maximum value?
38.25%289%2F10%29+=+-x%5E2+%2B+17x+-+34
34.425+=+-x%5E2+%2B+17x+-+34
0+=+-x%5E2+%2B+17x+-+68.425
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B17x%2B-68.425+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2817%29%5E2-4%2A-1%2A-68.425=15.3.

Discriminant d=15.3 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-17%2B-sqrt%28+15.3+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2817%29%2Bsqrt%28+15.3+%29%29%2F2%5C-1+=+6.54423927843921
x%5B2%5D+=+%28-%2817%29-sqrt%28+15.3+%29%29%2F2%5C-1+=+10.4557607215608

Quadratic expression -1x%5E2%2B17x%2B-68.425 can be factored:
-1x%5E2%2B17x%2B-68.425+=+-1%28x-6.54423927843921%29%2A%28x-10.4557607215608%29
Again, the answer is: 6.54423927843921, 10.4557607215608. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B17%2Ax%2B-68.425+%29