Determine the equation of the parabola with vertex (-3,6) and that passes through (2,-9)?

1 Answer
Jim G.
Apr 29, 2018

#y=-3/5x^2-18/5x+3/5#

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)=(-3,6)#

#rArry=a(x+3)^2+6#

#"to find a substitute "(2,-9)" into the equation"#

#-9=25a+6rArr25a=-15rArra=-3/5#

#rArry=-3/5(x+3)^2+6larrcolor(red)"in vertex form"#

#"distribute and simplify"#

#y=-3/5(x^2+6x+9)+6#

#color(white)(x)=-3/5x^2-18/5x-27/5+30/5#

#rArry=-3/5x^2-18/5x+3/5larrcolor(red)"in standard form"#

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