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zalisa [80]
3 years ago
13

The zeros of a quadratic function are 2 and 4 what is the vertex of the function

Mathematics
1 answer:
ZanzabumX [31]3 years ago
3 0

The x-coordinate of the vertex is precisely halfway between the given roots 2 and 4; thus, x = (2+4)/2, or x=3.  The y-coordinate is the value of the function at this x=3.  

We can actually determine the equation of this quadratic from the zeros:

f(x) = (x-2)(x-4), or   f(x) = x^2 - 6x + 8.  To find the y-coord. of the vertex,, subst. 3 for x in f(x) = x^2 - 6x + 8:    f(3) = 3^2 - 6(3) + 8 = 9 - 18 + 8, or -1.  Then we know that the vertex is at (3, -1).


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or another way to solve this is....

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Answer:

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And we can find this probability using the complement rule:

P(z>-2)=1-P(z

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(z>-2)=1-P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

X \sim N(440,20)  

Where \mu=440 and \sigma=20

We are interested on this probability

P(X>440)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>400)=P(\frac{X-\mu}{\sigma}>\frac{400-\mu}{\sigma})=P(Z>\frac{400-440}{20})=P(z>-2)

And we can find this probability using the complement rule:

P(z>-2)=1-P(z

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(z>-2)=1-P(z

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