Question

Write the quadratic function in vertex form: f(x) = 4x^2 + 2x-5​

Answer 1

Answer:

$f(x) = 4( {x + \frac{1}{2}) }^{2} - \frac{21}{4}$

Step-by-step explanation:

We want to rewrite

$f(x) = 4 {x}^{2} + 2x - 5$

in vertex form.

We factor 4 to get:

$f(x) = 4( {x}^{2} + \frac{x}{2} ) - 5$

We add and subtract half the square of the coefficient of x.

$f(x) = 4( {x}^{2} + \frac{x}{2} + \frac{1}{16} ) - 5 - 4 \times \frac{1}{16}$

We factor perfect square trinomial to get:

$f(x) = 4( {x + \frac{1}{2}) }^{2} - 5 - \frac{1}{4}$

$f(x) = 4( {x + \frac{1}{2}) }^{2} - \frac{21}{4}$