Given
#color(white)("XXX")y=2x^2+8x-4#
Our initial objective will be to convert this into "vertex-form",
namely #y=color(green)m(x-color(red)a)^2+color(blue)b# with vertex at #(color(red)a,color(blue)b)#
Setting aside the constant #(-4)# for a moment and extracting the #color(green)m# factor:
#color(white)("XXX")y=color(green)2(x^2+4x)color(white)("XXX")-4#
Completing the square:
#color(white)("XXX")y=color(green)2(x^2+4xcolor(magenta)(+4))color(white)("XX")-4color(magenta)(-(color(green)2xx4))#
Rewriting as a squared binomial and a simplified constant:
#color(white)("XXX")y=color(green)2(x+2)^2color(white)("XX")-12#
Express in explicit vertex form:
#color(white)("XXX")y=color(green)2(x-color(red)(""(-2)))^2+color(blue)(""(-12))#
#color(orange)("Vertex is at: "(color(red)(-2),color(blue)(-12))#
The y-intercept is the value of #y# when #x=0#.
Substituting #0# for #x# in the original equation :
#color(white)("XXX")y=2 * 0^2 - 8 * 0 -4#
gives the #color(cyan)("y-intercept at "y=-4# or, if you prefer at #color(cyan)(""(0,-4))#
graph{2x^2+8x-4 [-12.78, 12.53, -12.6, 0.06]}
