Question

find the x intercepts of a parabola with vertex (1,-108) and y intercept (0,-105)

Answer 1

long time since i done these...

Answer 2

general form is y = ax^2 + bx + c
when x = 0 , y = -105

so c = -105

Answer 3

x coordinate of the vertex = -b / 2a = 1

the y coordinate of the vertex = -108

so -108 = a*1^2 + b - 105

Answer 4

so b = -2a
and
-108 = a + b - 105

a + b = -3
substitute b = -2a in the above:
a - 2a = -3
-a = -3
a = 3

now finding b:
b = -3 -3 = -6

so equation is

3x^2 - 6x - 105 = 0

solve to find the x intercepts:

(3x - 21)(x + 5 ) = 0

x = 7 , -5

x intercepts are 7 and -5