What is how to find the vertex of a parabola?

Here's how to find the vertex of a parabola:

The vertex of a parabola is the point where the parabola changes direction. It's either the minimum point (if the parabola opens upwards) or the maximum point (if the parabola opens downwards). There are a couple of ways to find it:

1. Using the Vertex Form:

If the equation of the parabola is given in vertex form:

y = a(x - h)^2 + k

Then the vertex is simply the point (h, k). Remember that the h value is the opposite of what you see inside the parentheses.

2. Using the Standard Form:

If the equation is in standard form:

y = ax^2 + bx + c

You can find the x-coordinate of the vertex using the following formula:

x = -b / 2a

Once you have the x-coordinate, substitute it back into the original equation to find the y-coordinate of the vertex. This will give you the y-coordinate of the vertex.

Summary:

• Vertex Form: y = a(x - h)^2 + k => Vertex = (h, k)
• Standard Form: y = ax^2 + bx + c => Vertex = (-b/2a, f(-b/2a)) where f(x) = ax^2 + bx + c