Find a formula for the quadratic function whose graph has yi

Find a formula for the quadratic function whose graph has y-intercept at y = 15 and zeros at x = 3 and x = 5.

Solution

y = ax^2 +bx +c

y intercept : 15 = 0 +o +c

c = 15

y = ax^2 +bx +15

(zeros : ( 3,0) and ( 5,0)

0= 9a +3b +15

3a +b = -5 ---(1)

0 = 25a +5b +15

5a +b = -3 ---(2)

solve (1) and (2): 2a = 2; a =1

3+b = -5 ; b = -8

y = x^2 -8x +15