Question

The expression 3x^2-x-9 is rearranged into the form a(x+2)^2+b(x+2)+c. What are the values of a,b,and c?

Answer 1

3x^2-x-9=a(x+2)^2+b(x+2)+c
compare coefficent
now
a=?
b=?
c=?

Answer 2

You would first of all have to expand
a(x+2)^2 + b(x+2) + c
= a(x^2 + 4x + 4) + bx + 2b + c
= ax^2 + 4ax + 4a + bx + 2b + c
= ax^2 + (4a+b)x + (4a + 2b + c)
now compare:
3x^2 <---> ax^2 ---- a = 3

4a+b)x <---> -x
4a + b = -1
12+b = -1
b = -13

4a+2b+c = -9
12 - 26 + c = -9
c = 5


check:
3(x+2)^2 - 13(x+2) + 5
= 3(x^2 + 4x + 4) - 13x - 26 + 5
= 3x^2 + 12x + 12 - 13x - 26 + 5
= 3x^2 - x - 9 , as required

Answer 3

ooh yes yes very correct i know that