How do you write an equation of a parabola that has the vertex at point (2,7) and passes through the point (−1,3)?

1 Answer
Jim G.
May 7, 2018

#y=-4/9x^2+16/9x+47/9#

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)=(2,7)#

#rArry=a(x-2)^2+7#

#"to find a substitute "(-1,3)" into the equation"#

#3=9a+7rArr9a=-4rArra=-4/9#

#rArry=-4/9(x-2)^2+7larrcolor(red)"in vertex form"#

#"distributing and simplifying gives"#

#y=-4/9(x^2-4x+4)+7#

#rArry=-4/9x^2+16/9x+47/9larrcolor(red)"in standard form"#

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