Find the solutions of the followingg quadratic functions Fin

Find the solutions of the followingg quadratic functions:

Find the domain and range of each of the following function:

Domain:

Range:

Domain:

Range:

a) -3x^2 +2x +8 =0

factorise : -3x^2 +6x -4x +8 =0

-3x(x-2) -2(x-2) =0

(-3x -2)(x-2) =0

-3x = 2----> x= -2/3

x=2

Solution : x= -2/3 , 2

b) 2(x+3)^2 = 32

(x+3)^2 = 16

take square root on both sides:

x+3 = +/- 4

x = -7 , 1

a) f(t) = sqrt(4-7t)

Domain: 4 -7t >=0

7t<=4 ---->t <= 4/7

(- inf , 4/7)

Range : f(t) =0

[ 0, inf)

g(x) = -x^2 +9

Domain: all real (- inf, inf)

Range : y interecpt : y =9 and its an inverted parabola

So, (-inf ,9]