Question 1206388

Which quadratic function in vertex from can be represented by the graph that has 

the vertex at ({{{0}}}, {{{-4}}}) =>{{{h=0}}}, {{{k=-4}}}

passes through the point ({{{3}}},{{{ -7}}})=({{{x}}},{{{y}}})=>{{{x=3}}},{{{y=-7}}}

use vertex form formula

{{{y=a(x-h)^2+k}}}...substitute given {{{h=0}}}, {{{k=-4}}}
, {{{x=3}}},{{{y=-7}}}


{{{-7=a(3-0)^2-4}}}

{{{-7+4=9a}}}

{{{9a=-3}}}

{{{a=-3/9}}}

{{{a=-1/3}}}


go to

{{{y=a(x-h)^2+k}}}...substitute {{{a=-1/3}}}, {{{h=0}}}, {{{k=-4}}}

{{{y=-(1/3)(x-0)^2-4 }}}

{{{y=-(1/3)x^2-4 }}}


answer: A

{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(0,-4,.12),locate (0,-4,V(0,-4)),
circle(3,-7,.12),locate (3,-7,p(3,-7)),
graph( 600, 600, -10, 10, -10, 10, -(1/3)x^2-4)) }}}