Question 56717
find the maximum value of {{{y=-x^2+6x}}}
The maximum value of a parabola, whose coefficient of x^2 is negative, is it's vertex.
This quadratic equation is in standard for:{{{highlight(y=ax^2+bx+c)}}}, our a=-1, b=6, and c=0.
The equation for finding the x value of a quadratic equation written in standard form is: {{{highlight(x=-b/2a)}}}
{{{x=-(6)/(2(-1))}}}
{{{x=-6/-2}}}
{{{x=3}}}
Plug that into the parabola for x and you'll find the maximum value.
{{{y=-(3)^2+6(3)}}}
{{{y=-9+18}}}
{{{y=9}}}
The maximum value of this parabola is at (3,9).
Happy Calculating!!!