Question

i can write a quadratic equation in vertex form. i can graph a quadratic function. i can determine the axis of symmetry and vertex from a quadratic equation click here for a help video 7. complete the square to identify key parts of the following parabola and graph it on a coordinate plane, showing all work. $y = x^2 + 4x + 3$ a. vertex form of given equation:

Explanation:

Step1: Recall vertex form and completing the square

The vertex form of a quadratic is \( y = a(x - h)^2 + k \), where \((h,k)\) is the vertex. To complete the square for \( y = x^2 + 4x + 3 \), we take the coefficient of \( x \), which is 4, divide by 2 to get 2, and square it to get 4.

Step2: Rewrite the equation

We rewrite the equation by adding and subtracting the squared term: \( y = (x^2 + 4x + 4) - 4 + 3 \).

Step3: Simplify the equation

Simplify the perfect square trinomial and the constants: \( y = (x + 2)^2 - 1 \).

Answer:

\( y = (x + 2)^2 - 1 \)