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3 years ago

How do I rewrite a quadratic into graphing form

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

3 0

Step-by-step explanation:

Standard form of a quadratic is f(x) = ax² + bx + c.

To convert to vertex form, the simplest method is to find the x-coordinate of the vertex using h = -b/(2a).

Then, plug back into the equation to find the y-coordinate of the vertex. k = f(h).

Finally, the leading coefficient is the same as the standard form, a.

f(x) = a(x − h)² + k

Another method is to complete the square.

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A) 11 and 12 B) 8 and 9 C 10 and 11 D 76 and 78

Valentin [98]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Extension: Suppose that there is some positive number bb so that logb(5) = 0.84.

Papessa [141]

Answer:

b = 6.79

Step-by-step explanation:

Data provided:

logb(5) = 0.84

Now,

From the properties of log function

logₓ (z)= $\frac{\log(z)}{\log(x)}$ (where the base of the log is equal for both numerator and the denominator)

also,

log(xⁿ) = n × log(x)

thus,

using the above properties, we can deduce the results as:

logₓ(y) = n is equivalent to y = xⁿ

Thus,

logb(5) = 0.84

⇒ $\frac{\log(5)}{\log(b)}$ = 0.84

log(5) = 0.84 × log(b)

log(5) = $\log(b^{0.84})$ (as log(xⁿ) = n × log(x) )

taking the anti-log both sides

we get

5 = $b^{0.84}$

b = 6.79

8 0

4 years ago

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Sati [7]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

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.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

$\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

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

$Z = \frac{135 - 128}{23}$

$Z = 0.3$

$Z = 0.3$ has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

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

$Z = \frac{141 - 128}{23}$

$Z = 0.565$

$Z = 0.565$ has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

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

$Z = \frac{125 - 128}{23}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483

X = 120

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

$Z = \frac{120 - 128}{23}$

$Z = -0.35$

$Z = -0.35$ has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

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

$1.28 = \frac{X - 128}{23}$

$X - 128 = 1.28*23$

$X = 157.44$

157.44mmHg

6 0

3 years ago

X squared = 1/100 what is x? also x^3 = 343 what is x?

ioda

X is 1 over 10. 10 squared is 100. X is 7. The third root of 343 is 7.

7 0

3 years ago

1. The point (3, 1) is on the line whose equation is 2x + y = c. What is the value of c?

Otrada [13]

Answer:

c = 7

Step-by-step explanation:

Given

2x + y = c

Since (3, 1) is on the line then it makes the equation true,

Substitute x = 3, y = 1 into the equation

2(3) + 1 = c

6 + 1 = c

7 = c

8 0

3 years ago