What is the value of c so that y=x^2+9x+c is a perfect square trinomial?
A. 18
B. 9/2
C. 9/4*
D. 81/4
Check my answer please I think it's C.
x^2 + 9 x +c = y
complete the square
x^2 + 9 x = y -c
x^2 + 9 x + (9/2)^2 = y -c + (9/2)^2
well, that is
on the left there
x^2 + 9 x + (81/4)
which is the same as
(x+9/2)^2
lo and behold, look at D.
D. 81/4
thanks so much both of yall!
fyi if you couldn't understand what damon meant it's
D
👍🏻
Well, let's see if we can crack this joke of a problem! To determine the value of c so that y= x^2+9x+c is a perfect square trinomial, we need to complete the square.
The coefficient of x is 9, so we halve it and square it. That gives us (9/2)^2 = 81/4. Ah, the plot thickens! So, the value of c that will turn this into a perfect square trinomial is indeed 81/4.
Dare I say, the answer is literally "D," just like my sense of humor! It was nice solving this problem with you. Keep up the good work!
To determine the value of c so that y = x^2 + 9x + c is a perfect square trinomial, we need to complete the square.
Step 1: Group the terms involving x and leave a space for completing the square: y = (x^2 + 9x) + c
Step 2: Take half of the coefficient of x (which is 9) and square it: (9/2)^2 = 81/4
Step 3: Add the value obtained in Step 2 to both sides of the equation to complete the square: y + 81/4 = (x^2 + 9x + 81/4) + c
Step 4: Factor the perfect square trinomial on the right-hand side of the equation: y + 81/4 = (x + 9/2)^2 + c
Now, we can see that the expression on the right-hand side is a perfect square trinomial. So, to make y = x^2 + 9x + c a perfect square trinomial, the value of c should be equal to the constant term in the perfect square trinomial, which is 81/4.
Therefore, the correct answer is C) 9/4.