Question

Rewrite the function y=x²+2x+4 in vertex form.

Answer 1

The function y = x² + 2x + 4 in vertex form is y = (x + 1)² + 3. This is achieved by completing the square, which involves adding and subtracting the square of half the coefficient of x within the equation. The function y = x² + 2x + 4 in vertex form is y = (x + 1)² + 3.

Step-by-step explanation:

To rewrite the function y = x² + 2x + 4 in vertex form, we will complete the square. The vertex form of a quadratic function is y = a(x-h)² + k, where (h,k) is the vertex of the parabola. To complete the square:

1. Factor the leading coefficient from the x-terms if it is not 1 (in this case, it is 1, so we can skip this step).
2. Rearrange the equation as y = (x² + 2x) + 4.
3. Add and subtract the square of half the coefficient of x inside the parenthesis: y = (x + 1)² - 1 + 4.
4. Simplify the equation: y = (x + 1)² + 3.

The function y = x² + 2x + 4 in vertex form is y = (x + 1)² + 3.