Question

Find the vertex of the function.

f(x) = 3x^2 - 6x + 4

Answer 1

To find the vertex of the function, we need to rewrite the function in vertex form. The vertex form of a quadratic function is given by:

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

where (h,k) is the vertex of the parabola.

Given the function f(x) = 3x^2 - 6x + 4, we first need to complete the square to rewrite it in vertex form.

f(x) = 3(x^2 - 2x) + 4
f(x) = 3(x^2 - 2x + 1) + 4 - 3(1) (Adding and subtracting (b/2)^2, where b is the coefficient of x)
f(x) = 3(x^2 - 2x + 1) + 1

Now the function is in vertex form, with (h,k) = (1,1).

So the vertex of the function f(x) = 3x^2 - 6x + 4 is (1,1).