How to determine the rule of a parabola?

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Can someone please explain to me how to do question 3? Thank!

1 Answer
Jim G.
Dec 8, 2017

#y=3/2x^2+6x+10#

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 turning point"#
#"and a is a multiplier"#

#"here "(h,k)=(-2,4)#

#rArry=a(x+2)^2+4#

#"to find a substitute "(4,58)" into the equation"#

#58=a(6)^2+4rArra=54/36=3/2#

#rArry=3/2(x+2)^2+4larrcolor(red)"in vertex form"#

#"expanding and simplifying gives"#

#y=3/2(x^2+4x+4)+4#

#rArry=3/2x^2+6x+10larrcolor(red)"in standard form"#

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