Probability is the ratio of the times an event is likely to occur divided by the total possible events. In the case of our die, there are six possible events, and there is one likely event for each number with each roll, or 1/6. Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

5 0

3 years ago

find an equation in the form y=ax^2+bx+c for the parabola passing through the points. (2,28),(4,116),(-3,88)

IgorC [24]

<h3>Answer:</h3>

y = 8x² -4x +4

<h3>Explanation:</h3>

I find it quick and easy to let a graphing calculator do quadratic regression on the given points. It gives the coefficients of the equation directly. (See attached.)

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If you want to do this "by hand," you can substitute each of the x and y value pairs into the equation to get three linear equations in a, b, and c. These are generally easy to solve, as the "c" variable can be eliminated right away.

... 28 = a·2² +b·2 +c = 4a +2b +c

... 116 = a·4² +4b +c = 16a +4b +c

... 88 = a·(-3)² +b·(-3) +c = 9a -3b +c

Subtracting the first and third equations from the second, we have ...

... (16a +4b +c) -(4a +2b +c) = (116) -(28) ⇒ 12a +2b = 88

... (16a +4b +c) -(9a -3b +c) = (116) -(88) ⇒ 7a +7b = 28

Dividing the first of these reduced equations by 2, and the second by 7, we have ...

6a +b = 44
a +b = 4

Subtracting the second of these from the first gives ...

... (6a +b) -(a +b) = (44) -(4) ⇒ 5a = 40

From which we find

... a = 8

... b = 4 -a = 4 -8 = -4

We choose the first of the original equations to find c:

... c = 28 -4a -2b = 28 -4·8 -2(-4)

... = 28 -32 +8 = 4

With (a, b, c) = (8, -4, 4), the equation of the parabola is ...

... y = 8x² -4x +4

5 0

4 years ago