Question 48429
You don't mention if the intercepts are to be found by algebra or from your graph.


Anyway, to solve/plot {{{y<-2 (x-1)^2 + 2}}} you need to solve/plot {{{y=-2(x-1)^2 + 2}}}


To graph/plot it: pick various values of y. These are your choice. Pick something fairly obvious like -3, -2, -1, 0, 1, 2,3 and find the equivalent x-value for each. Plot these. Add more if you need them.


To find the intercepts algebraically:
{{{y=-2(x-1)^2 + 2}}}
{{{y=-2(x^2-2x+1) + 2}}}
{{{y=-2x^2+4x-2 + 2}}}
{{{ y=-2x^2+4x }}}


when x=0, y will by zero too. So curve passes through (0,0)


when y=0: {{{ -2x^2+4x = 0 }}}
{{{ -2(x^2-2x) = 0 }}}
{{{ x^2-2x = 0 }}}
{{{ x(x-2) = 0 }}}
so x=0 or x-2=0
x=0 or x=2


jon