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Convert the following function from standard from to vertex form. Show all of your work.

f(x) = x^2 + 7x — 1

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Answer:

Explanation:

To convert the function f(x) = x^2 + 7x - 1 from standard form to vertex form, we need to complete the square. The vertex form of a quadratic function is:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

To complete the square, we add and subtract (b/2a)^2 to the standard form of the quadratic function, where a is the coefficient of the x^2 term, and b is the coefficient of the x term. This gives us:

f(x) = x^2 + 7x - 1 + (49/4) - (49/4)

Now, we can group the x terms and factor the first three terms:

f(x) = (x^2 + 7x + (49/4)) - (49/4) - 1

Next, we can write the first three terms as a square of a binomial:

f(x) = (x + (7/2))^2 - (49/4) - 1

Finally, we can simplify the expression by combining the constant terms:

f(x) = (x + (7/2))^2 - (53/4)

Therefore, the function f(x) = x^2 + 7x - 1 in vertex form is:

f(x) = (x + (7/2))^2 - (53/4)

User Sean Goudarzi
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