How do you write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the point Vertex (-2,5); Point ( 0,9)?

1 Answer
Jim G.
Jul 20, 2018

#y=x^2+4x+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)=(-2,5)#

#y=a(x+2)^2+5#

#"to find a substitute "(0,9)" into the equation"#

#9=4a+5rArr4a=4rArra=1#

#y=(x+2)^2+5larrcolor(red)"in vertex form"#

#color(white)(y)=x^2+4x+4+5#

#y=x^2+4x+9larrcolor(red)"in standard form"#

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