Question

Find the vertex of the parabola is the vertex a minium or maxium f(x)1/3x(x+14)²+1?

a) (0, 0)
b) (14, 0)
c) (-14, 0)
d) Not enough information provided

Answer 1

d) Not enough information provided. The vertex of the parabola represented by the equation f(x)1/3x(x+14)²+1 is (-7, 1/3).

Step-by-step explanation:

To find the vertex of the parabola represented by the equation f(x) = 1/3x(x+14)²+1, we need to rewrite the equation in vertex form. The vertex form of a parabola is given by f(x) = a(x-h)² + k, where (h, k) represents the vertex. In this case, a = 1/3.

To rewrite the equation in vertex form, we complete the square. We have f(x) = 1/3(x+7)² + 1/3. Therefore, the vertex is (-7, 1/3). Since the coefficient of x² is positive, the parabola opens upwards and the vertex represents the minimum point. So, the correct answer is (c) (-7, 1/3).