a group of 25 sixth graders, 40% of them said they had never visited another state. How many students said they had never visite
2 answers:
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The standard form of a quadratic equation is 
, while the vertex form is:
, where (h, k) is the vertex of the parabola.
What we want is to write
as
First, we note that all the three terms have a factor of 3, so we factorize it and write:
.
Second, we notice that
are the terms produced by 
, without the 9. So we can write:
, and substituting in we have:
![\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20y%3D3%28x%5E2-6x-2%29%3D3%5B%28x-3%29%5E2-9-2%5D%3D3%5B%28x-3%29%5E2-11%5D)
.
Finally, distributing 3 over the two terms in the brackets we have:
![y=3[x-3]^2-33](https://tex.z-dn.net/?f=y%3D3%5Bx-3%5D%5E2-33)
.
Answer:
What we want is to write
First, we note that all the three terms have a factor of 3, so we factorize it and write:
Second, we notice that
Finally, distributing 3 over the two terms in the brackets we have:
Answer:
We will proceed to solve each case to determine the solution of the problem.
<u>case a)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case a) is not the solution of the problem
<u>case b)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case b) is not the solution of the problem
<u>case c)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case c) is not the solution of the problem
<u>case d)</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
therefore
case d) is the solution of the problem
therefore
<u>the answer is</u>