Identifying the Vertex of y=x²+2x: Finding Minimum or Maximum?

To determine whether the quadratic function $y = x^2 + 2x$ has a minimum or maximum point, we need to examine its structure and calculate the vertex.

Step 1: Identify the structure of the quadratic function.

The given function is $y = x^2 + 2x$, which is a standard form quadratic function $y = ax^2 + bx + c$ where $a = 1$, $b = 2$, and $c = 0$.

Step 2: Calculate the vertex.

The vertex of a quadratic function is given by $x = -\frac{b}{2a}$. Substituting the values of $a$ and $b$ into this formula gives:

$x = -\frac{2}{2 \times 1} = -1$.

Substitute $x = -1$ back into the original equation to find the y-coordinate of the vertex:

$y = (-1)^2 + 2(-1) = 1 - 2 = -1$.

Therefore, the vertex is at the point $(-1, -1)$.

Step 3: Determine if the vertex is a minimum or maximum.

Since the coefficient $a = 1$ is positive, the parabola opens upwards. This means that the vertex represents the lowest point on the graph, which is a minimum point.

Therefore, the solution to this problem is that the parabola has a minimal point.