Which of the following is the minimum value of the equation y = 3x^2 − 4x − 2?
1 answer:
Answer:
-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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<em>Confirmation</em>
You can also use a graphing calculator to show you the minimum.
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so the 5 gallons ones is 40% acid, how much acid solute is in it anyway? well just 40% of 5 or namely 0.4*5 = 2 gallons.
the 3 gallons one is 50%, likewise it has 0.50 * 3 = 1.5 gallons of acid solute in it.