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3 years ago

Y=x^2-2x-5 vertex form

Mathematics

1 answer:

slamgirl [31]3 years ago

5 0

Hey there! I'm happy to help!

First, we'll want to find the vertex of this parabola.

Given the equation y=ax^2+bx+c, the formula for the x-coordinate of the vertex is always $-\frac{b}{2a}$ .

In our equation here, our a is 1 and our b is -2.

$-\frac{-2}{2}=\frac{2}{2}=1$

Now that we have our x-value of our vertex, we can plug it into our equation to find our y-coordinate.

y=1²-2(1)-5

y=1-2+5

y=-1+5

y=4

So, our vertex is at (1,4).

Vertex form is y=a(x-h)²+ k where (h,k) is our vertex. We know now that our vertex is (1,4) and we also know that our a is 1, so we can simply plug it in to this equation.

y=(x-1)²+4

Have a wonderful day and keep on learning! :D

You might be interested in

(cot^2x - 1)/(csc^2x) = cos2x

Alex787 [66]

Answer:

Step-by-step explanation:

The idea here is to get the left side simplified down so it is the same as the right side. Consequently, there are 3 identities for cos(2x):

$cos(2x)=cos^2x-sin^2x$ ,

$cos(2x)=1-2sin^2x$ , and

$cos(2x)=2cos^2x-1$

We begin by rewriting the left side in terms of sin and cos, since all the identities deal with sines and cosines and no cotangents or cosecants. Rewriting gives you:

$\frac{\frac{cos^2x}{sin^2x} -\frac{sin^2x}{sin^2x} }{\frac{1}{sin^2x} }$

Notice I also wrote the 1 in terms of sin^2(x).

Now we will put the numerator of the bigger fraction over the common denominator:

$\frac{\frac{cos^2x-sin^2x}{sin^2x} }{\frac{1}{sin^2x} }$

The rule is bring up the lower fraction and flip it to multiply, so that will give us:

$\frac{cos^2x-sin^2x}{sin^2x} *\frac{sin^2x}{1}$

And canceling out the sin^2 x leaves us with just

$cos^2x-sin^2x$ which is one of our identities.

5 0

3 years ago

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters tha

uranmaximum [27]

Answer:

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

0.933 = 93.3% probability that the second machine produces an acceptable cork.

The second machine is more likely to produce an acceptable cork.

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.

What is the probability that the first machine produces an acceptable cork?

The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm, which means that $\mu = 3, \sigma = 0.1$

Acceptable between 2.9 and 3.1, which means that this probability is the pvalue of Z when X = 3.1 subtracted by the pvalue of Z when X = 2.9.

X = 3.1

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

$Z = \frac{3.1 - 3}{0.1}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 2.9

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

$Z = \frac{2.9 - 3}{0.1}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)

For the second machine, we have that $\mu = 3.04, \sigma = 0.04$ . Same probability we have to find out. So

X = 3.1

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

$Z = \frac{3.1 - 3.04}{0.04}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 2.9

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

$Z = \frac{2.9 - 3.04}{0.04}$

$Z = -3.5$

$Z = -3.5$ has a pvalue of 0.0002

0.9332 - 0.0002 = 0.933

0.933 = 93.3% probability that the second machine produces an acceptable cork.

Which machine is more likely to produce an acceptable cork?

Second one has a higer probability, so it is more likely to produce an acceptable cork.

6 0

3 years ago

2 4/7 divided by 1 3/6 =

Rudiy27

Answer:

Step-by-step explanation:

2,57 divided by 1.5 equals

1.713

7 0

1 year ago

Read 2 more answers

The ratio of red to blue marbles in a bag is 2:5. If there are 65 blue marbles in the bag, how many red marbles are there? Let x

hoa [83]

Answer:

first get the total ratio; 2 + 5 = 7

so the fraction of blue marbles is 5/7

then assume the number of total marbles to be k

then use the expression;

5/7*k = 65

7*5/7 * k = 65*7

5k =455

5/5k = 455/5

k = 91

then calculate the number if red marbles from;

x = 2/7*91

x = 26

Therefore there are 26 red marbles.

8 0

3 years ago

Please answer it now in two minutes

Pepsi [2]

Answer:

m∠C = 90°

Step-by-step explanation:

Triangle BDC is a right triangle with the measure of angle D = 90°

By applying Cosine rule in the given triangle,

Since, Cosine of any angle in a right triangle is a ratio of Its adjacent side and Hypotenuse (Opposite side of the right angle)

CosC = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

CosC = $\frac{\text{DC}}{\text{BC}}$

CosC = $\frac{7}{8}$

$C=\text{Cos}^{-1}(\frac{7}{8})$

C = 28.955

C = 29°

Therefore, m∠C = 29° will be the answer.

4 0

3 years ago