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Determine the vertex by completing the square. Show process.

y = x^2 -6x + 28

y = x^2 -6x + 28

= x^2 - 6x + 9 - 9 + 28 , took half of the 6, squared it, then added and subtracted it

= (x - 3)^2 + 19

so the vertex is .....

Did you know?

Did you know that you can determine the vertex of a quadratic equation by completing the square? By following this method, you can find the exact coordinates of the highest or lowest point on the parabolic curve. Let's take the equation y = x^2 - 6x + 28 as an example. To complete the square, we manipulate the equation to the form (x - h)^2 + k, where (h, k) represents the coordinates of the vertex. In this case, we start by rearranging the equation to y = (x^2 - 6x) + 28. Then, we take half of the coefficient of the x-term (-6/2 = -3) and square it to get 9. Adding and subtracting 9 inside the parentheses, we have y = (x^2 - 6x + 9 - 9) + 28. Simplifying gives us y = (x - 3)^2 - 9 + 28. Thus, the vertex is located at (3, 19), with x = 3 representing the axis of symmetry and y = 19 as the minimum value of the quadratic function. By completing the square, you can easily find the vertex and gain a deeper understanding of quadratic equations!