Find the vertex of the function given below y=x^2-2x+1

Mathematics

1 answer:

Ymorist [56]3 years ago

3 0

Hey there! :)

Answer:

(1, 0).

Step-by-step explanation:

Convert from standard form to vertex form by completing the square:

y = x² - 2x + 1

Move 1 to the other side:

-1 = x² - 2x

Complete the square. Remember to add to both sides:

-1 + (1) = x² -2x + 1

Simplify:

0 = (x - 1)²

The function in vertex form is:

y = (x - 1)²

Therefore, the vertex is:

(1, 0).

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d1i1m1o1n [39]

Answer:

a) 96.64% probability that maximum speed is at most 50 km/h

b) 24.67% probability that maximum speed is at least 48 km/h

c) 86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 46.8, \sigma = 1.75$