Question 421228
find the vertex, the line of symmetry, the max or minimum value
of the quadratic function, and graph the function.

{{{f(x) =-2x^2 + 2x + 4}}}

the equation for a parabola can also be written in "vertex form":


{{{f(x)= -2(x-h)^2 + k}}}....the vertex of the parabola is the point (h, k)


{{{-b/2a}}} gives the {{{x-coordinate}}} of the vertex


{{{-2/2(-2)=-2/-4=1/2}}}


so, {{{x-coordinate}}} is {{{1/2}}}


Substituting in the original equation to get the y-coordinate, we get:


{{{f(x)= -2(1/2)^2 + 2(1/2) + 4}}}


{{{y= -2(1/4) + 1 + 4}}}


{{{y= -1/2 + 1 + 4}}}


{{{y= 1/2  + 4}}}


{{{y= 4.5}}}


So, the vertex of the parabola is at (1/2, 4.5). 



*[invoke hummingbird_min_max_test1 "x", -2, 2, 4]