3. write an equation in which the quadratic expression 2x^2-2x-12 equals 0. show the expression in factored form and explain what your solutions mean for the equation. show your work.

Step-by-step explanation:

2x²-2x-12 = 2 (x²-x - 6)

 but : x²-x - 6 = x² - 2(1/2)x +(1/2)² - (1/2)² - 6

                      = ( x - 1/2)² - 1/4 - 6

                        =  ( x - 1/2)² - 25/4

x²-x - 6 = ( x - 1/2)² - (5/2)²

by identity ; a² - b² = (a - b ) ( a +b)

x²-x - 6 = ( x - 1/2 - 5/2)  ( x - 1/2 +5/2)

x²-x - 6 = (x - 3) (x +2)

so :  2x²-2x-12 =2(x - 3) (x +2) = (2x-6)(x+2) (factored form)

now :  2x²-2x-12 = 0   : 2x - 6 = 0    or x+2 = 0

x= 3 or x = - 2  two solutions

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~