Question

Write y=x²-10x+28 in vertex form, then identify the vertex.

Answer 1

To write y = x² - 10x + 28 in vertex form, y = (x - 5)² + 3, we complete the square. The vertex of the parabola is (5, 3).

Step-by-step explanation:

To write the quadratic equation y = x² - 10x + 28 in vertex form, we need to complete the square. Here are the steps:

1. Factor out the coefficient of the x² term if it is not 1 (in this case, it is already 1, so we don't need to factor anything).
2. Rewrite the quadratic term and linear term, leaving space for the square term: y = (x² - 10x + ___) + 28 - ___.
3. Take half of the coefficient of the x term (which is -10), square it (5² = 25), and add that inside the parenthesis: y = (x² - 10x + 25) + 28 - 25.
4. Simplify the equation by combining like terms outside the parenthesis: y = (x - 5)² + 3.

The equation is now in vertex form. The vertex of this parabola is the point (h,k), which can be found inside the parenthesis and the constant term. Here, h = 5 and k = 3, so the vertex is (5, 3).