Help me on this math question and please include how you solved it

A = 0
b = 1
x = -5

ax + 16 = b - 3x

sub -5 for x
-5a + 16 = b - 3(-5)
-5a + 16 = b + 15

Double negatives above makes a positive

solve for b

-5a + 1 = b

sub b into equation -5a + 16 = b + 15

-5a + 16 = -5a + 16

Both sides cancel out so a = 0

Sub 0 for a in -5a + 1 = b

-5(0) + 1 = b

1 = b

Confirm

By replacing all values in original equation

(0)(-5) + 16 = 1 - 3(-5)

16 = 16

The vertex of the quadratic function is (1.5, -.75)