Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form. his answer is f(x) = ()2 – 5.

1) The vertex form of a quadratic function is:

y = A(x - h)^2 + k, where h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

2) The function given is: f(x) = x^2 + 6x + 4

3) To find the vertex form of that equation you have to complete squares.

These are the steps fo complete squares:

a) You will work with the first two terms: x^2 + 6x

b) divide the coefficient of the x term by 2, form the square binomial with x and the and the half of the coefficient, and subtract the square of the half of the coefficient to keep the equality. This is how you do that:

=> 6/2 = 3

=> x^2 + 6x = (x + 3)^2 - 9

c) include the third term of the trinomial:

=> x^2 + 6x + 4= (x + 3)^2 - 9 + 4

=> x^2 + 6x + 4 = (x + 3)^2 - 5

4) The vertex form of f(x) is (x + 3)^2 - 5

5) You can prove that by expanding the square binomial to come back to the orignal form of the fucntion:

(x + 3)^2 - 5 = x^2 + 2(3)(x) + 9  - 5 = x^2 + 6x + 4, which is what you wanted to prove.



The vertex form of x^2 + 6x + 4 is (x + 3)^2 - 5.

Where the vertex is ( - 3, - 5)

The objects do not reach terminal velocity         there is not enough time from the time the object falls from when it hits the ground to achieve terminal velocity. an object must be placed higher to achieve terminal velocity in order to be in free fall.