Answer :
Answer:
c is the square of half of b
Step-by-step explanation:
A quadratic equation can be written in the following form:
[tex]ax^2+bx+c[/tex].
Based off of the information provided, we can test to see if which answer choice is correct.
OPTION A IS INCORRECT:
Although, for [tex]x^2+6x+9[/tex], c is 1.5 times b, we do not see that relationship reflected in other equations, such as [tex]x^2+10x+25[/tex] and [tex]x^2+12x+36[/tex]. There must be a different relationship.
OPTION B IS INCORRECT:
Although c is double b for x^2+8x+16, this rule is not applicable for the rest of the equations. C is double b for the is 1.5 times that of b for x^2+6x+9, and for and for x^2+10x+25, c is 2.5 times b, and for x^2+12x+36, c is 3 times of b.
OPTION C IS CORRECT:
We can test this relationship based off of the information given.
for x^2+6x+9, c equals (6/2)^2 which is 9
for x^2+8x+16, c equals (8/2)^2 which is 16
for x^2+10x+25 c equals (10/2)^2 which is 25
and finally, for x^2+12x+36 c equals (12/2)^2 which is 36.
OPTION D IS INCORRECT:
C is not the square of B.
for x^2+6x+9, b^2 which is 36 (c here is 9)
for x^2+8x+16, b^2 is 64 (c here is 16)
for x^2+10x+25 b^2 is 100 (c here is 25)
and finally, for x^2+12x+36 b^2 is 144 (c here is 36).