# How do you write #f(x) = x^2 + 7x + 2# in vertex form?

In vertex form:

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To write the function ( f(x) = x^2 + 7x + 2 ) in vertex form, complete the square.

Start by rearranging the terms to group the ( x ) terms together:

[ f(x) = (x^2 + 7x) + 2 ]

Next, complete the square for the ( x^2 + 7x ) term by adding and subtracting ((\frac{7}{2})^2 = \frac{49}{4}):

[ f(x) = (x^2 + 7x + \frac{49}{4}) - \frac{49}{4} + 2 ]

Now, rewrite the expression inside the parentheses as a perfect square:

[ f(x) = (x + \frac{7}{2})^2 - \frac{49}{4} + 2 ]

Simplify:

[ f(x) = (x + \frac{7}{2})^2 - \frac{49}{4} + \frac{8}{4} ]

Combine the constant terms:

[ f(x) = (x + \frac{7}{2})^2 - \frac{41}{4} ]

So, the function ( f(x) = x^2 + 7x + 2 ) in vertex form is ( f(x) = (x + \frac{7}{2})^2 - \frac{41}{4} ).

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