All categories

3 years ago

F(x) = 5x2 – 20x + 26 In vertex form

Mathematics

1 answer:

mihalych1998 [28]3 years ago

6 0

Answer:

$f(x)=5(x-2)^{2}+6$

Step-by-step explanation:

we have

$f(x)=5x^{2} -20x+26$

This is the equation of a vertical parabola open upward

The vertex is a minimum

The equation of a vertical parabola in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

(h,k) is the vertex

Convert the given function to vertex form

Factor the leading coefficient

$f(x)=5(x^{2} -4x)+26$

Complete the square

$f(x)=5(x^{2} -4x+4)+26-20$

$f(x)=5(x^{2} -4x+4)+6$

Rewrite as perfect squares

$f(x)=5(x-2)^{2}+6$ ------> equation in vertex form

The vertex is the point (2,6)

You might be interested in

I have a 74 average in my math class, And I get a 100 on my quarter finals exam the exam is 30 percent of my grade what is my gr

KonstantinChe [14]

Answer:

u will have a 100 meaning a A+

Step-by-step explanation:

5 0

3 years ago

One of the authors with too much time on his hands weighed each chocolate candy in a bag of 463 plain chocolate candies. Complet

wel

Answer:

a. One of the chocolate candies weighed 0.776 gram and it was heavier than 25 of the other chocolate candies. What is the percentile of this particular value?

It is the 5th percentile.

b. One of the chocolate candies weighed 0.876 gram and it was heavier than 329 of the other chocolate candies. What is the percentile of this particular value?

It is the 71th percentile.

c. One of the chocolate candies weighed 0.856 gram and it was heavier than 229 of the other chocolate candies. What is the percentile of this particular value?

It is the 49th percentile.

Step-by-step explanation:

So when we are talking about percentile, what it means is the point below a certain score or percentage lies, or the rank.

The formula is simple:

Let's call percentile pth, pth= $\frac{p}{100}*(n+1)$

where p is the position in the data set you want to evaluate (in statistical analysis, these are called quartiles, and they are useful for evaluating groups, so 3 quartiles would divide sample into 25th, 50th and 75th, four quartiles would be 20th, 40th, 60th, 80th, and so on).

and n is the number of elements in the set

For this problem there are no quartiles specified, but we can then work with the definition of percentile, meaning, if you are the 5th percentile, then 95% of the group are above you.

a. So 0.776 was heavier than 25 others, meaning it is in the 26th position out of 463. But we need that in relation to 100, so $\frac{26}{463}$ is 0.0562 or about 5/100, (rounded down). That would mean that the percentile is:

pth= $\frac{26}{463}$ *100=5.62 or 5, rounded down

b. 0.876 was heavier than 329 others, meaning it is in the 330th position out of 463. In relation to 100, so $\frac{330}{463}$ is 0.7127 or about 71/100, (rounded down). That would mean that the percentile is:

pth= $\frac{330}{463}$ *100=71.27 or 71, rounded down

c. 0.856 was heavier than 229 others, meaning it is in the 230th position out of 463. In relation to 100, so $\frac{230}{463}$ is 0.4967 or about 49/100, (rounded down). That would mean that the percentile is: