Complete the square to make a perfect square trinomial. Write the result as a binomial square. q2−23q

The perfect square form of the given expression will be .

The given expression is .

It is required to write the given expression as a perfect square polynomial or trinomial.

We will use the identity .

So, the first term from the given expression will be .

To find the second term b, divide the 2nd term of the given expression by 2,

So, the given expression can be written in the perfect square form as,

Therefore, the perfect square form of the given expression will be .

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Step-by-step explanation:

Given the expression:

To complete the square, we follow these steps:

Step 1: Identify the coefficient of q

Coefficient of q=-23

Step 2: Divide the coefficient of q by 2

Step 3: Square your result from step 2 and add it to the equation

This gives us:

We have now completed the square.

Step 4: Write the result as a binomial square.

To write it as a binomial square, pick the variable and add the term in the bracket.

Therefore:

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.