Answer:
[tex]f(x) = 4( {x + \frac{1}{2}) }^{2} - \frac{21}{4} [/tex]
Step-by-step explanation:
We want to rewrite
[tex]f(x) = 4 {x}^{2} + 2x - 5[/tex]
in vertex form.
We factor 4 to get:
[tex]f(x) = 4( {x}^{2} + \frac{x}{2} ) - 5[/tex]
We add and subtract half the square of the coefficient of x.
[tex]f(x) = 4( {x}^{2} + \frac{x}{2} + \frac{1}{16} ) - 5 - 4 \times \frac{1}{16} [/tex]
We factor perfect square trinomial to get:
[tex]f(x) = 4( {x + \frac{1}{2}) }^{2} - 5 - \frac{1}{4} [/tex]
[tex]f(x) = 4( {x + \frac{1}{2}) }^{2} - \frac{21}{4} [/tex]
