Which of the following is the minimum value of the equation y = 3x^2 − 4x − 2? -3 1/3 2 3 -2/3

-3 1/3

Step-by-step explanation:

The quadratic

... y = ax² +bx +c

has its extreme value at

... x = -b/(2a)

Since a = 3 is positive, we know the parabola opens upward and the extreme value is a minimum. (We also know that from the problem statement asking us to find the minimum value.) The value of x at the minimum is -(-4)/(2·3) = 2/3.

To find the minimum value, we need to evaluate the function for x=2/3.

The most straightforward way to do this is to substitue 2/3 for x.

... y = 3(2/3)² -4(2/3) -2 = 3(4/9) -8/3 -2

... y = (4 -8 -6)/3 = -10/3

... y = -3 1/3

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Confirmation

You can also use a graphing calculator to show you the minimum.

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)

b and c

step-by-step explanation: