Question

If the Vertex is (-2,13) ; point (3,10) what is the quadratic function

Answer 1

y =ax^2 + bx + c ;
- b / 2a = - 2 ; then, b = 4a;
- ( b^2 - 4ac ) / 4a = 13 ; then, -b^2 + 4ac = 52a ; then, - 16a^2 + 4ac = 52a; then
-16a + 4c = 52 ; then, -4a + c = 18 ;
10 = 9a + 3b + c ; then, 10 = 9a + 12a +c ; then, 10 = 21a + c ;
We solve the system :
-4a + c = 18 ;
-21a - c = - 10 ;
____________(+)
-25a = 8;
a = -8 / 25 ;
c = 10 - 21 × ( - 8 / 25 ) ;
c = 10 + 168 / 25 ;
c = 418 / 25 ;
b = 4 × ( - 8 / 25 ) ;
b = -32 / 25 ;
y = ( - 8 /25 )x^2 + ( -32 / 25 )x + 418 / 25 ;