How To Find The Equation of a Quadratic Function From a Graph

TL;DR

Learn how to find the equation of a quadratic function from a given graph using either the vertex form or standard form.

Transcript

in this video we're going to talk about how to find the equation of a quadratic function from a graph so here we're given a graph and we could tell that each Mark goes by two and we're given two points on a graph for this point here has an x value of four and a y value of negative 2. and this point is the vertex which is at three negative four so g... Read More

Key Insights

• 💁 There are two forms of quadratic equations that can be used to find the equation of a quadratic function from a graph: vertex form and standard form.
• 🤩 The vertex form equation (y = a(x-h)^2 + k) requires the knowledge of the vertex and one additional point on the graph.
• 😀 The standard form equation (y = ax^2 + bx + c) needs three points on the graph to find the quadratic function.
• 😒 The vertex form equation is easier to use when the vertex and one more point are known.
• 😃 The standard form equation involves finding the coefficients a, b, and c using systems of equations or elimination method.
• ❣️ By knowing the x and y intercepts, the value of c can be determined in the standard form equation.
• 💁 To convert from vertex form to standard form, expand and simplify the equation by using the multiplication property.

Questions & Answers

Q: What are the two forms of quadratic equations that can be used to find the equation of a quadratic function from a graph?

The two forms are the vertex form (y = a(x-h)^2 + k) and the standard form (y = ax^2 + bx + c).

Q: How many points are needed to find the equation using the vertex form equation?

With the vertex form equation, you only need the knowledge of the vertex and one additional point on the graph.

Q: What are the values of H and K used in the vertex form equation?

H represents the x-coordinate of the vertex, and K represents the y-coordinate of the vertex.

Q: How many points are needed to find the equation using the standard form equation?

The standard form equation requires three points on the graph to find the quadratic function.

Q: What are the steps to convert the equation from vertex form to standard form?

To convert from vertex form to standard form, you need to expand and simplify the equation by using the multiplication property.

Summary & Key Takeaways

• Given two points on a graph, the vertex and another point, you can use the vertex form or standard form equation to find the quadratic function.

• Using the vertex form equation (y = a(x-h)^2 + k), knowing the vertex and one more point is enough to find the equation.

• Using the standard form equation (y = ax^2 + bx + c), you need three points to find the quadratic function.