So, to find the x intercepts we first set x to 0 to get:
[tex] 0=-4x^2+12x-8 [/tex]
Then, notice that all the terms are divisible by -4 so we can divide it out to get:
[tex] 0=x^2-3x+2 [/tex]
Now, we want to see what two numbers add to -3 and multiply to 2. These two numbers have to both be negative, and the only two factors of 2 are 2 and 1, so our two numbers are -1 and -2. Now, we split -3x into -x and -2x and finish factoring:
[tex] 0=x^2-x-2x+2 \implies \\
0=x(x-1)-2(x-1) \implies \\
0=(x-2)(x-1) \implies \\
x-1=0\implies x=1\\
x-2=0 \implies x=2 \\
x=1,x=2 [/tex]
Our two x intercepts would be (1,0) and (2,0).
