Question 936233

the vertex form:

{{{y=a(x-h)^2+k}}}

{{{y=-2x^2-12x-10}}}

{{{y=-2(x^2+6x)-10}}}

{{{y=-2(x^2+6x+_)-_-10}}}

{{{y=-2(x^2+6x+9)-2*(-9)-10}}}

{{{y=-2(x+3)^2+18-10}}}

{{{y=-2(x+3)^2+8}}}

vertex is at ({{{-3}}},{{{-19}}})


y-intercept is {{{8}}}

x-intercept is:

{{{0=-2x^2-12x-10}}}

{{{2x^2+12x+10=0}}}

{{{2x^2+2x+10x+10=0}}}

{{{(2x^2+2x)+(10x+10)=0}}}

{{{2x(x+1)+10(x+1)=0}}}

{{{(2x+10)(x+1)=0}}}

{{{2(x+5)(x+1)=0}}}

solutions:

if {{{(x+5)=0}}}=> {{{x=-5}}}

if {{{(x+1)=0}}}=> {{{x=-1}}}

so, x-intercepts are: {{{x=-5}}} and {{{x=-1}}}


{{{ graph( 600, 600, -10, 10, -15, 10, -2x^2-12x-10) }}}