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1 solution
Let's write the above quadratic as: y = ( x − 2 p ) 2 + ( 3 6 − 2 p 2 ) with vertex at ( 2 p , 3 6 − 2 p 2 ) . The locus of these vertices can then be expressed as:
y = − a x 2 + b ⇒ − a ( 2 p ) 2 + b = − 2 p 2 + 3 6 ⇒ − 4 a p 2 + b = − 2 p 2 + 3 6 ⇒ a = 2 1 , b = 3 6
such that a b = 1 8 .