What is the equation of the parabola that has a vertex at # (-6, 3) # and passes through point # (12,9) #?
1 Answer
Aug 3, 2018
Explanation:
#"the equation of a parabola in "color(blue)("vertex form"# is.
#•color(white)(x)y=a(x-h)^2+k#
#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a multiplier"#
#"here "(h,k)=(-6,3)#
#y=a(x+6)^2+3#
#"to find a substitute "(12,9)" into the equation"#
#9=18a+3#
#18a=9-3=6rArra=6/18=1/3#
#y=1/3(x+6)^2+3larrcolor(red)"in vertex form"#
#"distributing gives"#
#y=1/3(x^2+12x+36)+3#
#y=1/3x^2+4x+15larrcolor(red)"in standard form"#
