Answer:
[tex]f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4} [/tex]
Explanation:
The given function is
[tex]f(x) = - 4 {x}^{2} - 2x - 3[/tex]
To write the function is vertex form, we need to complete the square.
We first factor -4 to get:
[tex]f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3[/tex]
Add and subtract the square of half the coefficient of x.
[tex]f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3[/tex]
We factor the perfect square trinomial and simplify to get:
[tex]f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4} [/tex]
