Functions f(x) and g(x) are shown below: f(x) g(x) f(x) = 3x2 + 12x + 16 graph of sine function which starts at 0 comma 0 and decreases to the minimum pi over 2, then increases to the maximum of 3 pi over 2 then decreases to 2 pi where the cycle repeats courtesy of texas instruments using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value.

g(x) has the smallest minimum y-value

Step-by-step explanation:

f(x) is the equation of a parabola

The general form of a parabola is ax² + bx + c, if a is positive, the parabola has a minimum. The minimum is at the vertex, the x-coordinate of the vertex is calculated as follows: -b/2a.  For this case, x =-12/(2*3) = -2, which corresponds to the following function value: 3(-2)² + 12(-2) + 16 = 4

g(x) is the sine function

The sine function is a periodic function which oscillates between -1 and 1