Question

The correct answer?

Answer 1

See below.

Explanation:

Expanding

`a(x+r)^2+s = a(x^2+2rx+r^2)+s = a x^2+2arx+a r^2+s`

and now comparing coeficients

`{(a=3),(2ar=-18),(ar^2+s=-1):}`

and solving we get

`a = 3`
`r = -18/(2 xx 3) = -3`
`s = -1-ar^2 = -1-27 = -28`

so the answer is A

Answer 2

`A`

Explanation:

First, we pay attention to `3x^2-18x`

We see that the coefficients share `3` as their GCF.

We can therefore rewrite this as:

`3(x^2-6x)-1`

Now, we look at the coefficient of `-6x`

The coefficient is `-6`

We now divide the coefficient by two, then square the result.

`=>(-6/2)^2=9`

`3(x^2-6x)-1` add `9` inside the parenthesis.

`3(x^2-6x+9)-1` Since we added `9` in the parenthesis, we need to make an adjustment.

We do so by multiplying `9` by the number in front of parenthesis, then subtracting it from the entire expression.

`=>3(x^2-6x+9)-1-27`

`=>3(x^2-6x+9)-28`

Factor the expression in the parenthesis.

Therefore, we now have:

`=>3(x-3)^2-28`

The answer to this problem is `-28` or `A`