Question

Explain how to convert f(x) into the general, vertex form of the equation. Use complete sentences.
x2+6x+1

Answer 1

Find the vertex of x^2 + 6x + 1. Then insert a = 1 and vertex (h,k) into the equation

y = a(x - h)^2 + k

Answer 2

I don't understand may you explain

Answer 3

That's the easy way to do it, but since you probably have to complete the square, you should do it that way instead.

Answer 4

to complete the square take half the coefficient of x ( half of 6 = 3) and write
(x + 3)^2

to make this equal to x^2 + 6x we need to subtract 3^2 :-
x^2 + 6x = (x + 3)2 - 9
now we add the 1
x^2 + 6x + 1 = (x+3)^2 - 9 + 1 = (x +3)^2 - 8

which is the vertex form

the vertex is at the point (-3,-8)
(compare with Hero's formula)

Answer 5

and how do you find the solutions

Answer 6

you have it there - you wanted the vertex form

Answer 7

do you want the zeroes of the function as well?

Answer 8

yes

Answer 9

(x +3)^2 - 8 = 0
(x +3)^2 = 8

now take the square root of each side of the equation

(remember the positive and negative square root of 8)

Answer 10

the rest is easy