All categories

3 years ago

How to Find the vertex of f(x)=-8x^2-8x+7

Mathematics

1 answer:

charle [14.2K]3 years ago

7 0

Answer:

The answer to your question is: (1/2, 5)

Step-by-step explanation:

Parabola f(x) = 8x² - 8x + 7

y = 8x² - 8x + 7

Vertical Parabola equation

( x - h)² = 4p (y - k) Transform the original equation to this form

8x² - 8x = y - 7

8(x² - x + ( )²) = y - 7 Complete squares

8 (x² - x + (1/2)²) = y - 7 + 2 Simplification

8 (x² - x + 1/4) = y - 5

(x - 1/2)² = 1/8 (y - 5)

Finally Vertex

(1/2 , 5)

You might be interested in

Look at these numbers. 0.3,

timama [110]

0.3.......the 3 is in the tenths place
0.103....the 3 is in the thousandths place
0.13.....the 3 is in the hundredths place

0.3 is ur answer

8 0

3 years ago

Read 2 more answers

Examine the required sample size needed to be able to

Xelga [282]

Answer:

$n=(\frac{2.33(500)}{10})^2 =13572.25 \approx 13573$

And if we use a sample level of n =2000 the margin of error would be higher as we can see here:

$ME=2.33\frac{500}{\sqrt{2000}}=26.05$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=500$ represent the population standard deviation assumed

n represent the sample size (variable of interest)

Confidence =98% or 0.98

ME = 10 represent the margin of error desired

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =10 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.33$ , replacing into formula (b) we got: