The vertex form of the equation is f(x) = 8(x + 1/4)^2 - 1/2
How to write the function in vertex form?
The equation is given as:
f(x) = 8x^2 + 4x
Factor out 8
f(x) = 8(x^2 + 1/2x)
Take the coefficient of x
k = 1/2
Divide by 2
k/2 = 1/4
Square both sides
(k/2)^2 = 1/16
Add and subtract the above expression to the bracket
f(x) = 8(x^2 + 1/2x + 1/16 - 1/16)
Expand
f(x) = 8(x^2 + 1/2x + 1/16) - 1/2
Rewrite as a perfect square
f(x) = 8(x + 1/4)^2 - 1/2
Hence, the vertex form of the equation is f(x) = 8(x + 1/4)^2 - 1/2
Read more about vertex forms at:
https://brainly.com/question/18797214
