Question #04862

1 Answer
Jim G.
Dec 9, 2017

#y=-2x^2-12x-10#

Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a multiplier"#

#"here "(h,k)=(-3,8)#

#rArry=a(x+3)^2+8#

#"to find a substitute "(0,-10)" into the equation"#

#-10=9a+8rArra=(-18)/9=-2#

#rArry=-2(x+3)^2+8larrcolor(red)"in vertex form"#

#"expanding and simplifying gives"#

#y=-2(x^2+6x+9)+8#

#rArry=-2x^2-12x-10larrcolor(red)"in standard form"#

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