Question

Find the zeros of g(x) = -x^2 + 6x - 8

Answer 1

(Remember to set g(x) to zero).

For this, I will be completing the square. Firstly, what two terms have a product of 8x^2 and a sum of 6x? That would be 4x and 2x. Replace 6x with 2x + 4x: $0=-x^2+2x+4x-8$

Next, factor -x^2 + 2x and 4x - 8 separately. Make sure that they have the same quantity on the inside of the parentheses: $0=-x(x-2)+4(x-2)$

Next, you can rewrite the equation as $0=(-x+4)(x-2)$

Now apply the Zero Product Property:

$-x+4=0\\-x=-4\\x=4\\\\x-2=0\\x=2$

The zeros of this equation are 4 and 2.