Question

Find the other x-intercept for the parabola defined by this equation: y=-4x^2+12x-8

Answer 1

So, to find the x intercepts we first set x to 0 to get:

$0=-4x^2+12x-8$

Then, notice that all the terms are divisible by -4 so we can divide it out to get:

$0=x^2-3x+2$

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:

$0=x^2-x-2x+2 \implies \\ 0=x(x-1)-2(x-1) \implies \\ 0=(x-2)(x-1) \implies \\ x-1=0\implies x=1\\ x-2=0 \implies x=2 \\ x=1,x=2$

Our two x intercepts would be (1,0) and (2,0).