Write 1/3 x^2 - 4x + 17 in vertex form

f(x)=−4(x+ 41 ) 2 − 4 11

Explanation:

The given function is

f(x) = - 4 {x}^{2} - 2x - 3f(x)=−4x 2 −2x−3

To write the function is vertex form, we need to complete the square.

We first factor -4 to get:

f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3f(x−4(x2 + 21 x)−3

Add and subtract the square of half the coefficient of x.

f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3f(x)=−4(x 2 + 21 x+ 16 1 )− 41 −3

We factor the perfect square trinomial and simplify to get:

f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4}f(x)=−4(x+ 41 ) 2 − 4 11

where are the choices?

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step-by-step explanation: