write equation of parabola that has vertex (-3,0) and goes through point (-5,4)

Question

write equation of parabola that has vertex (-3,0) and goes through point (-5,4)

 

please  show work

Answer 1

 

y = f(x) = ax² + bx + c   ;

vertex : [ (x=-3 = -b/2a ; f(-3)= 0 = a (-3)²+b(-3)+c ] ;

4 = a(-5)²+b(-5)+c

 

b=6a

9a - 3b + c = 0

25a-5b + c =4

 

9a - 18a + c = 0 -----> c = 9a

 

25a-30a + 9a = 4

 

4a = 4 ------> a = 1 -----> b = 6 -----> c = 9

 

The desired equation is f(x) = x² + 6x + 9