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3 years ago

Write the quadratic function in the form f (x)= a (x - h)' + k. f (x) = 3x² - 6x+6

Mathematics

1 answer:

Vlad1618 [11]3 years ago

6 0

Answer:

$f(x) = 3(x - 1)^2-3$

Step-by-step explanation:

Given

$f(x) = 3x^2 - 6x + 6$

Required

Write as:

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

In $f(x) = 3x^2 - 6x + 6$ , the coefficient of x is -6

Divide by 2: -3

Square: 9

Add 9 - 9 to the above equation

$f(x) = 3x^2 - 6x +9-9+ 6$

Split to 2

$f(x) = [3x^2 - 6x +9]-[9- 6]$

$f(x) = [3x^2 - 6x +9]-[3]$

Factorize:

$f(x) = [3x^2 - 3x -3x+9]-[3]$

$f(x) = [3x(x - 1) -3(x-1)]-[3]$

$f(x) = [(3x - 3)(x-1)]-[3]$

Factorize 3x - 3

$f(x) = [3(x - 1)(x-1)]-[3]$

$f(x) = 3(x - 1)^2-[3]$

$f(x) = 3(x - 1)^2-3$

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Does anyone know how to do this help please

statuscvo [17]

Answer:

$\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}$

Step-by-step explanation:

A quadratic function is given to us . And we need to fill out the table by using the function . The given function is ,

$\rm\implies y = x^2+x - 6$

Here we need to substitute the different values of x , to get the different values of y.

Put x = -3 :-

$\rm\implies y = 3^2-3-6\\$

$\rm\implies y = 9 - 3 - 6 \\$

$\rm\implies y = 0$

Put x = -2 :-

$\rm\implies y = 2^2-2-6\\$

$\rm\implies y = 4 -2-6\\$

$\rm\implies y = -4$

Put x = -1 :-

$\rm\implies y = -1^2-1-6\\$

$\rm\implies y = 1 -1-6 \\$

$\rm\implies y = -6$

Put x = 1 :-

$\rm\implies y = 1^2+1-6\\$

$\rm\implies y = 2 -6$

$\rm\implies y = -4$

Put x = 2 :-

$\rm\implies y = 2^2+2-6\\$

$\rm\implies y = 4 +2-6\\$

$\rm\implies y = 2$

Put x = 3 :-

$\rm\implies y = 3^2+3-6\\$

$\rm\implies y = 9 +3-6\\$

$\rm\implies y = 6$

Final table :-

$\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}$

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Step-by-step explanation:

Remember the 3:4:5 rule.

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Alexandra [31]

If the probability that a household owns a pet is 0.55 then the probability that all households will have pets is equal to 0.0503.

Given that the probability that a household owns a pet is 0.55 and there are 5 houses on a block.

We are required to calculate the probability that all the five households will have pets.

Probability is basicallly the chance of happening an event among all the events possible. It cannot be negative.

Binomial probability distribution is basically the probability calculations but in different combinations.

In this we have to calculate the probability that all the houses will have the pets then the probability that all five households will have pets is equal to $5C_{5}(0.55)^{5} (1-0.55)^{0}$

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Hence the probability that all the five households will have pets is equal to 0.0503.

Learn more about probability at brainly.com/question/24756209

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Step-by-step explanation:

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