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.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: