How do you write the quadratic in vertex form given #x^2-7x + 9#?

To write the quadratic in vertex form, you can complete the square. Start by finding the value of "h" in the vertex form equation ( y = a(x - h)^2 + k ) using the formula ( h = -\frac{b}{2a} ). In the given quadratic ( x^2 - 7x + 9 ), "a" is 1, "b" is -7. So, ( h = -\frac{-7}{2(1)} = \frac{7}{2} ). Next, substitute this value of "h" into the equation to find "k", which represents the vertex's y-coordinate. Plug "h" into the original equation and solve for "k". ( y = x^2 - 7x + 9 ) ( y = (x - \frac{7}{2})^2 + k ) ( y = x^2 - 7x + \frac{49}{4} + k ) Now, since we know that the quadratic's coefficient for the x term is -7, and we've already completed the square, the ( k ) term is the constant term left over. In this case, ( k = \frac{49}{4} ). Therefore, the quadratic equation in vertex form is ( y = (x - \frac{7}{2})^2 + \frac{49}{4} ).