Question 46106
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^2 + 17x - 34}}}
{{{x = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{x = (-17 +- sqrt( 17^2 - 4*-1*-34 ))/(2*-1) }}}
{{{x = (-17 +- sqrt( 289 - 136 ))/(-2) }}}
{{{x = (-17 +- 3*sqrt( 17 ))/(-2) }}}
{{{x = 8.5 +- 1.5*sqrt( 17 ) }}}
{{{8.5 - 1.5*sqrt( 17 ) <= x <= 8.5 + 1.5*sqrt( 17 )}}}
{{{graph(600,600,-4,16,-4,39,-x^2 + 17x - 34)}}}
What is the range of x values where y is at 90% of its maximum value?
{{{38.25(9/10) = -x^2 + 17x - 34}}}
{{{34.425 = -x^2 + 17x - 34}}}
{{{0 = -x^2 + 17x - 68.425}}}
*[invoke quadratic "x", -1, 17, -68.425]