Question

Consider the quadratic function. f(x) = px (q-x), where p and q are positive integers. The graph of y = f(x) passes through the point (6,0). the vertex of the function is (3, 27) Find the value of p.

Answer 1

p=3 and q = 6

Explanation:

f(x) = px (q-x) = pxq -x²p

f(x) = -px² + pqx

you have the system : f(6) = 0........(*)

f(3) = 27.....(**)

(*) means : when x =6 y = 0 : -p(6)² + pq(6) = 0 .... -36p +6pq =0

(**) means : when x =3 y = 27 : -p(3)² +pq(3) = 27........ -9p +3pq = 27

so the system : -6p +pq =0...(1)

-3p +pq = 9 ...(2)

by (1) : pq = 6p

by(2) : pq = 3p +9

so : 6p =3p+9

3p = 9

p=3 put this value in (1) : -6(3)+3q =0

3q =18

q=6 so : f(x) = -3x²+18x

*PICTURE ATTACHED*