Question

X2 + 4x + 3 rewrite the quadratic function in vertex form

Answer 1

Rewriting the quadratic equation x^2 + 4x + 3 in vertex form involves completing the square, resulting in (x + 2)^2 - 1, which indicates the vertex of the parabola is (-2, -1).

Step-by-step explanation:

To rewrite the quadratic function x^2 + 4x + 3 in vertex form, we need to 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. Here's how we rewrite the given quadratic equation step-by-step:

1. Start with the original equation, y = x^2 + 4x + 3.
2. Since the coefficient of x^2 is 1, we only need to focus on the x-terms. To complete the square, take half of the coefficient of x, square it, and add it to and subtract it from the expression to maintain equality. The number we need is (4/2)^2 = 4.
3. So, we have y = (x^2 + 4x + 4) - 4 + 3.
4. Now, we can recognize the expression in the parentheses as a perfect square: (x + 2)^2. So, we rewrite the equation as y = (x + 2)^2 - 1.
5. The equation is now in vertex form, with vertex (-2, -1).

This method is a standard way to convert a quadratic function to vertex form, which can be especially useful for graphing and analyzing the properties of the function.