What is the equation of the parabola that has a vertex at # (2, -5) # and passes through point # (-8,-7) #?

1 Answer
Jim G.
Oct 5, 2017

#y=-1/50(x-2)^2-5#

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)=(2,-5)#

#rArry=a(x-2)^2-5#

#"to find a substitute "(-8,-7)" into the equation"#

#-7=100a-5#

#rArra=-1/50#

#rArry=-1/50(x-2)^2-5larrcolor(red)" in vertex form"#

#"distributing and collecting like terms"#

#y=-1/50x^2+2/25x-127/25larrcolor(red)" in standard form"#

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