Finding the vertex of a parabola example | Quadratic equations | Algebra I | Khan Academy

TL;DR

Learn how to find the vertex of a quadratic equation by using the formula for the x-coordinate or by completing the square.

Transcript

I have an equation right here. It's a second degree equation. It's a quadratic. And I know its graph is going to be a parabola. Just as a review, that means it looks something like this or it looks something like that. Because the coefficient on the x squared term here is positive, I know it's going to be an upward opening parabola. And I am curiou... Read More

Key Insights

• ❎ The vertex of a quadratic equation can be found using the formula -b/2a or by completing the square.
• ☺️ The x-coordinate of the vertex is the value halfway between the roots of the equation.
• ❎ Completing the square involves adding a term to the equation to convert it into a perfect square trinomial.
• 💁 The vertex form of a quadratic equation is in the form (x-h)^2 + k, where (h, k) represents the vertex coordinates.
• ❣️ The y-coordinate of the vertex can be calculated by substituting the x-value of the vertex back into the equation.
• 😥 The vertex represents the minimum or maximum point of the parabola, depending on its concavity.
• ☺️ The quadratic formula can also be used to find the x-intercepts of a quadratic equation.

Questions & Answers

Q: How can you determine whether the graph of a quadratic equation is an upward or downward opening parabola?

The coefficient of the x squared term determines the concavity of the parabola. If it is positive, the parabola opens upward; if it is negative, the parabola opens downward.

Q: What is the formula for finding the x-coordinate of the vertex of a quadratic equation?

The x-coordinate of the vertex is given by the formula -b/2a, where b is the coefficient of the x term and a is the coefficient of the x squared term.

Q: How can the y-coordinate of the vertex be calculated?

The y-coordinate of the vertex can be found by substituting the x-value of the vertex back into the equation.

Q: What is completing the square, and how does it help in finding the vertex of a quadratic equation?

Completing the square involves manipulating the quadratic equation to create a perfect square trinomial. By doing this, the vertex form of the equation is obtained, which allows for easy identification of the vertex.

Summary & Key Takeaways

• The graph of a quadratic equation is a parabola that can open upwards or downwards.

• The vertex of an upward-opening parabola is the minimum point, while for a downward-opening parabola, it is the maximum point.

• The x-coordinate of the vertex can be found using the formula -b/2a, and the y-coordinate can be calculated by substituting the x-value back into the equation.