Question 1084015

Which function's graph has a vertex at ({{{-3}}},{{{-4}}})and contains the point ({{{-6}}},{{{-7}}})?

use vertex formula {{{y=a(x-h)^2+k}}} where {{{h}}} and {{{k}}} are coordinates of the vertex
A. 
{{{y=-(1/3)(x+3)^2-4}}}...-> {{{h=-3}}} and {{{k=-4}}}; so, this function has a vertex at ({{{-3}}},{{{-4}}})

now check the point ({{{-6}}},{{{-7}}})
{{{-7=-(1/3)(-6+3)^2-4}}}
{{{-7=-(1/3)(-3)^2-4}}}
{{{-7=-(1/cross(3))cross(9)3-4}}}
{{{-7=-3-4}}}
{{{-7=-7}}}-> since true, this is your answer


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-6,-7,.12),locate(-6,-7,p(-6,-7)),
 graph( 600, 600, -10, 10, -10, 10, -(1/3)(x+3)^2-4)) }}}

no need to check other options
B. 
{{{y=-(1/3)(x-3)^2-4}}}-> not answer
C. {{{y=-3(x-3)^2-4}}}-> not answer
D. {{{y=-3(x+3)^2-4}}}-> not answer