To convert the quadratic function f(x) = x2 + 3x + 2 into vertex form, we will complete the square. The vertex form of a quadratic equation is given as:
f(x) = a(x – h)2 + k,
where (h, k) is the vertex of the parabola.
Here are the steps to convert our function:
- Start with the original equation:
- f(x) = x2 + 3x + 2
- To complete the square, we need to focus on the x terms. Take the coefficient of x (which is 3), divide it by 2 (giving you 1.5), and then square it:
- (1.5)2 = 2.25
- Add and subtract this value inside the equation:
- f(x) = (x2 + 3x + 2.25) – 2.25 + 2
- This rewrites the equation as:
- f(x) = (x + 1.5)2 – 0.25
- Now we have the equation in vertex form:
- f(x) = (x + 1.5)2 – 0.25
From this form, we can identify the vertex of the quadratic function. The vertex (h, k) is given by:
- h = -1.5
- k = -0.25
Hence, the vertex of the parabola represented by the function f(x) is (-1.5, -0.25). This vertex form allows us to easily identify the vertex and understand the graph’s characteristics.