How to find the value of r ?

A quadratic function #f(x)=-3x^2 +kx +12# , where #k# is a constant, has maximum point #(2,r)# . Find the values of #k# and #r# .

1 Answer
Jim G.
Aug 30, 2017

#k=12,r=24#

Explanation:

#"substitute " (2,r)" into the equation"#

#r=-12+2k+12rArrr=2kto(color(red)(1))#

#"let x = 0 for y-intercept"#

#rArry=12larrcolor(red)" y-intercept"#

#"the equation in "color(blue)"vertex form"# is.

#y=-3(x-2)^2+r#

#"substitute "(0,12)" into the vertex form of the equation"#

#12=-12+rrArrr=24#

#"from "(color(red)(1))#

#r=2krArrk=1/2r=12#

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