Answer:
Explanation:
Remark
Unless you know calculus, the only way to solve this is by completing the square.
Solution
y = 4x^2 + bx - 2
y = 4(x^2 + b/4 ) - 2
y = 4(x^2 + b/4 + (1/2b/4)^2 ) - 2 - 4*(b/8)^2
y = 4(x^2 + b/4 + (b/8)^2 ) - 2 - b^2/16
y = 4(x + b/8)^2 - 2 - b^2/16
Now what you want to happen is to give b/8 a value of 1 so that when x is put in -1 you get 0 for what is inside the brackets.
b/8 = 1
b = 8
y = 4(x + 1)^2 - 2 - (8)^2 / 16
y = 4(x + 2)^2 - 2 - 4
y = 4(x + 1)^2 - 6
The vertex is at (-1, - 6)
The axis of symmetry is x = - 1
Note
This could have been done a lot shorter just by realizing that the number inside the brackets had to be + 1 as in (x + 1). But then you would not have been able to know the minimum value for y which is - 6