Graph y = (x-2) (x-4)

Parabola

Step-by-step explanation:

Simplify the expression y = (x - 2) x (x - 4)

Move terms, move variables to the left side and change their signs y=x2 - 6x + 8

-y2 + 6x + y = 8

Move variables to their right side and change its sign - x2 + 6x = 8 - y

Use the commutative properly to reorder th terms - x2 + 6x = y + 8

Multiply both sides - 1 - x2 - 6x = y - 8

To complete the square, the same value needs to be added to both sides x2 - 6x + ? = y - 8 + ?

Add 9 to right side x2 - 6x + 9 = y - 8 + 9

Using a2 - 2ab + b2 = (a - b) 2 factor the expression (x - 3) 2 = y - 8 + 9 calculate the sum (x-3) 2 = y+1

Since the equation can be written in form (x-k) 2 = 4px (y = h), the equation represents parabola