Question 213455
Rewrite:
y=8x+1-4x^2
as:
y = -4x^2+8x+1
.
There are two ways to do it.  By "completing the square" OR by find the "axis of symmetry".
.
I'll do the latter.  The "axis of symmetry" defines a line which divides the parabola right down the middle.  Once you know that, you can determine the vertex.
.
"axis of symmetry" is found by plugging in the values to:
-b/(2a) (derives from a portion of the quadratic equation)
-8/(2*(-4))
-8/-8
-1
Our axis of symmetry is then at:
x = -1
.
We now have half of our vertex: (-1, __)
to find the y coordinate, subsititute -1 for 'x' into the equation and solve for y:
y = -4x^2+8x+1
y = -4(1)^2+8(1)+1
y = -4+8+1
y = 5
.
Solution:
Vertex is at (-1, 5)