Question

Study the equation: y = +(x + 2)(x – 6).

Answer 1

For part A the x intercepts are -2 and 6

The x intercepts are whatever in the equation make y equal to zero.

Proof:

(-2)+2(x-6)
0(x-6)=0

Anything times 0 equals zero

Part B. The vertex is (2,-16)

Explanation: this one is a little hard to find but here it goes.

First use foil to multiply the 2 binomials

x^2-4x-12 now you have to factor it in a square.

This is kinda hard to grasp probably but if you subtract 4 from the -12 you get -16 but you cant just do that. I will show you how to do it

x^2-4x-12=y
x^2-4x-16=y-4

Now that we got that add it back to the other side, just separate from the -16

x^2-4x-16=y-4
x^2-4x+4-16=y

Now its still equal to the original equation just we have a perfect square now. So lets factor the perfect square.

(x-2)^2-16=y

Now to find the vertex just take the number in the perfect square (-2) and change its sign.

x=2

And -16 will be our y

x=2
y=-16


Part C you will have to do yourself. You can use a graphing calculator or online graphing software to do it.


Brainliest my answer if it helps you out?