consider the equation y=1/4 (x+2) (x-6). Is it easier to find the x-intercepts of this equation or the vertex? why?

x intercepts are easier. They are almost just read.

Step-by-step explanation:

The x intercepts are easier to find. You can almost just read them.

x + 2 = 0 Subtract 2 from both sides.

x = - 2 Answer

x - 6 = 0 Add 6 to both sides.

x = 6 Answer

So the x intercepts are (6,0) and (-2,0)

Now to the vertex. You could average the two x intercepts. But that will give you only the x value of the vertex. (6 - 2) / 2 = (4) / 2 = 2

But you still have to get the y value.

y (2) = (1/4) * (x + 2) (x - 6) Substitute 2 in for both xs

y (2) = (1/4) * (2 + 2) (2 - 6) Combine the terms

y (2) = (1/4) * 4 * - 4 multiply the 1/4 * 4 which gives 1

y (2) = 1 * - 4 = - 4

The vertex is (2,-4)

Note: If you do this the long way. The 1/4 has to be taken into account. Here we don't have to. The final result is

y = (1/4) (x - 2) ^2 - 4

and even then, the - 4 gives some trouble. The x intercepts are much easier.