y = 3(x + 4)^2 + 31
Step-by-step explanation:
We can convert the given quadratic equation into its vertex form by completing the square:
y = 3x^2 + 24x + 43
= 3(x^2 + 8x) + 43
= 3(x^2 + 8x + 4) + 31
= 3(x + 4)^2 + 31
This is the vertex form of the given quadratic equation with (-4, 31) as its vertex
Your good its 80 one way you can always tell if its a triangle is if all the angles add up to 180
You want to end up with 
. Expand this using the angle sum identity for sine:
We want this to line up with 
. Right away, we know 
.
We also need to have
Recall that 
for all 
; this means
Then
So we end up with
