Complete the square to re-write the quadratic function in vertex form:y, equals, x, squared, plus, 10, x, minus, 2y=x 2 +10x−2

Sure, let's complete the square step by step to rewrite the quadratic function in vertex form.

Given the quadratic function: $y = x^2 + 10x - 2$

1. Isolate the constant term: $y = x^2 + 10x - 2$

2. Complete the square:

   • Take the coefficient of $x$, which is 10.
   • Divide it by 2: $\frac{10}{2} = 5$.
   • Square it: $5^2 = 25$.

3. Add and subtract this square inside the equation: $y = x^2 + 10x + 25 - 25 - 2$

4. Group the perfect square trinomial and the constants: $y = (x^2 + 10x + 25) - 27$

5. Rewrite the perfect square trinomial as a binomial squared: $y = (x + 5)^2 - 27$

So, the quadratic function in vertex form is: $y = (x + 5)^2 - 27$