How do you find the maximum or minimum of #y+3x^2=9#?

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Answer 1 · 2018-05-23T12:08:13

Maximum value of #y=9# at #x=0#

# y +3 x^2 =9 or y = -3 x^2 +9 or y= -3(x-0)^2+9#.

This is equation of parabola opening downward since coefficient of

# x^2 # is negative. So minimum value will be #- oo# and

maximum value will be at vertex. Comparing with vertex form of

equation #f(x) = a(x-h)^2+k ; (h,k)# being vertex we find

here #h=0 , k=9 :.# Vertex is at #(0,9) #

Therefore the minimum value of function is #- oo# and

maximum value of function is #y=9 # at #x=0#

graph{y+ 3x^2=9 [-22.5, 22.5, -11.25, 11.25]} [Ans]