How to Find the Vertex of a Quadratic Function

TL;DR

Learn how to find the vertex of a quadratic function using a formula step by step.

Transcript

hello in this video we're going to find the vertex of f of x equals negative 2x squared minus 12x plus 3. so this is a quadratic function let's go ahead and work through its solution the first thing we want to do is match this up with the following form so this is really f of x equals 8X squared plus BX plus C and this will allow us to identify a a... Read More

Key Insights

• 💁 Understanding how to match a quadratic function to the standard form is crucial for finding the vertex.
• ❓ The formula for finding the vertex simplifies the process by directly providing the coordinates.
• ☺️ The x-coordinate of the vertex is determined by calculating -B/2A.
• ❣️ The y-coordinate is found by substituting the x-coordinate into the original function.
• 🥺 The vertex represents the maximum or minimum point of the parabola depending on the leading coefficient.
• 💦 This method works for any quadratic function and provides a reliable way to find the vertex.
• 🧘 The vertex coordinates (-3, 21) provide insight into the shape and position of the parabola.

Questions & Answers

Q: How do you identify the coefficients of a quadratic function?

To find the coefficients, match the function to the form f(x) = ax^2 + bx + c and identify a and b directly from the equation.

Q: What is the formula for finding the vertex of a quadratic function?

The formula for the vertex is (-B/2A, f(-B/2A)), where B is the coefficient of x and A is the coefficient of x^2.

Q: How do you find the x-coordinate of the vertex using the formula?

Compute -B/2A to find the x-coordinate of the vertex, which represents the axis of symmetry of the parabola.

Q: How do you find the y-coordinate of the vertex in a quadratic function?

Substitute the x-coordinate into the original function to find the y-coordinate, completing the vertex coordinates.

Summary & Key Takeaways

• Identify the coefficients of the quadratic function.

• Use the formula to find the x-coordinate of the vertex.

• Substitute the x-coordinate to find the y-coordinate and determine the vertex.