simplify the following expression.

(x+1)^2-3(x+2)

a. x^2-3x+7
b. x^2-x-5
c. x^2-3x-5
d. x^2-x+3

simplify the following expression.

(5x^3y^-)

a. -30x^7y^2
b. -30x^12y^3
c. -30x^12/y^3
d. -30x^7/y^2

solve the following equation.

8+x/2 - x+3/3=4

a. x=-14
b. x=6
c. x=14
d. x=-6

solve the equation.

x^2-3x-8=x+4

a. x=-6 or x=2
b. x=1+ sqrt5 or x=1- sqrt5
c. x=1+2sqrt3 or x=1-2sqrt3
d. x=-2 or x=6

joseph is solving the equation x^2+8x-4=0 using the technique completing the square.
x^2+8x-4=0
x^2+8x+? =4+?
what number should joseph add to both sides of the equation to complete the square, and why?

a. he should add 4 to both sides because 8/2=4.
b. he should add 4 to both sides because (4/2)^2=4.
c. he should add 16 to both sides because 16/2=8.
d. he should add 16 to both sides because (8/2)^2=16.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

answer: the answer is e

step-by-step explanation: