A is a U-shaped curve that is formed by a quadratic equation. It is a common type of mathematical function that appears in various calculations, such as in physics and engineering.

The of a parabola is a critical point that determines its shape, direction, and axis of symmetry. It is the highest or lowest point on the parabolic curve and is located at the intersection of the axis of symmetry and the parabola. To calculate the vertex of a parabola, we need to consider its standard form, which is given as:

y = ax^2 + bx + c

where a, b, and c are constants, and x and y are variables.

The formula to find the vertex of a parabola is:

x = -b/2a
y = f(x)

where x and y are the coordinates of the vertex, and f(x) is the value of the function at x.

The first step in the vertex of a parabola is to determine the values of a, b, and c in its standard form. For example, let’s consider the parabola y = 2x^2 + 4x – 3. Here, a = 2, b = 4, and c = -3.

The next step is to use the formula x = -b/2a to find the x-coordinate of the vertex. In our example, we have:

x = -4/2(2) = -1

Therefore, the x-coordinate of the vertex is -1.

The final step is to substitute the value of x into the given function to find the y-coordinate of the vertex. In our example, we have:

y = 2(-1)^2 + 4(-1) – 3 = -1

Therefore, the y-coordinate of the vertex is -1.

Thus, the vertex of the parabola y = 2x^2 + 4x – 3 is (-1, -1).

Note that the vertex of a parabola can also be found by completing the square or using the quadratic formula. However, the formula x = -b/2a provides a simpler and more straightforward method to determine the vertex.

In summary, the vertex of a parabola is an essential point that helps to understand its behavior and properties. It is determined by the standard form of the parabolic equation and can be calculated using the formula x = -b/2a. By knowing how to find the vertex of a parabola, we can effectively solve various real-world problems and enhance our mathematical skills.

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