Good evening.
The simetry axis can be found with the vertex in x formula:
[tex]\mathsf{x_V = -\dfrac{b}{2a}}[/tex]
Whe take from the function:
a = -16
b = 48
So:
[tex]\mathsf{t_v = -\dfrac{48}{2\cdot (-16)}}\\ \\ \mathsf{t_v = \dfrac{-48}{-32}}\\ \\ \\ \boxed{\mathsf{t_v = \dfrac{3}{2}}}[/tex]
We can conclude that the axis of simetry is the line with the equation:
t = 3/2
It represents that if we take two points at the same x-distance to this line, they will have the same image(value in h).
For example:
t' = 3/2 + 1/2 = 4/2 = 2
t'' = 3/2 - 1/2 = 2/2 = 1
We calculate h(t):
[tex]\mathsf{h(x') = -16.{1}^2+48.1}\\ \\ \mathsf{h(x') = -16 + 48 = 32}\\ \\ \\ \mathsf{h(x'') = -16.2^2 + 48.2}\\ \\ \mathsf{h(x'')=-64 + 96=32} [/tex]
Where we can se the same h-value.
Doubts? Please, comment :)
