Question 89994
Determine the maximum or minimum range value of the function:
{{{P(x) = -3x^2+6x+5}}}
First, since the coefficient of the {{{x^2}}} term is <0 (negative), the parabola described by the functions opens downward so you know that the vertex will occur at the maximum.
To find the x-coordinate of the vertex, use:
{{{x = -b/2a}}} in this equation, a = -3, and b = 6.
{{{x = -6/2(-3)}}}
{{{x = 1}}} Now substitute this value of x into the quadratic equation and solve for y to get the y-coordinate of the vertex.
{{{y = -3(1)^2+6(1)+5}}} Simplify.
{{{y = -3+6+5}}}
{{{y = 8}}}
The vertex is at (1, 8) and is a maximum.
{{{graph(300,200,-5,5,-5,10,-3x^2+6x+5)}}}