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



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

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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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