Question

I desperately need help
1.f(x) = (x-3)(x-2)
g(x) = (x - sqrt(2)(x-sqrt(3))
h(x) = (x-2i)(x-3i)
#2: Explain how to convert f(x) into the general, vertex form of the equation. Use complete sentences. You may use the f(x) you created in question 1 as an example.

#3: Find the solutions of g(x). Show each step.

#4: Justify if completing the square is a good method for solving when the Discriminant is negative. Use any of your three functions as an example and respond in complete sentences.

Answer 1

#2:
Converting f(x) into the general form of a quadratic formula with the vertex of the parabola located at (h, k):
a) Multiply out the two factors given as the definition of f(x): (x-3)(x-2):
f(x) = x^2 - 5x + 6. Rewrite as f(x) = x^2 - 5x + 6.
b) Complete the square: x^2 - 5x - (5/2)^2 + (5/2)^2 + 6
c) Simplify: (x - 5/2)^2 25/4 + 6
1*(x- 5/2)^2 + 49/4
d) Compare to: a*(x - h)^2 + k
where (h, k) is the vertex of the parabola
e) Identify h as 5/2 and k as 49/4
f) f(x) in re-written form is (x - 5)^2 + 49/4; the vertex of the parabola is at (5/2, 49/4).
Note also: by setting f(x) = (x-3)(x-2) = to 0, we find that the horizontal intercepts of the graph are (3,0) and (2,0).

Answer 2

In regard to #3: Simply set g(x) = 0 and solve for the two x values at which this function is zero.