Question

Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1

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Maude

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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)

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