Which function in vertex form is equivalent to f(x) = x2 + x +1? f(x) = (x + one-quarter) squared + three-quarters f(x) = (x + one-quarter) squared + five-quarters f(x) = (x + one-half) squared + three-quarters f(x) = (x + one-half) squared + five-quarters

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

x² + x + 1 ← to obtain vertex form use metod of completing the square

To complete the square

add/ subtract (half the coefficient of the x- term )² to x² + x

x² + 2()x + - + 1

f(x) = (x + )² + ← in vertex form

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!