Writing Quadratic Equations In Vertex Form & Standard Form Given 3 Points

TL;DR

Learn how to write quadratic equations in standard form and vertex form using given points.

Transcript

in this video we're going to focus on writing quadratic equations in standard form and vertex form so let's say if you're given three points 1 comma 0 and let's say 2 comma 1 and 3 comma 6 how can you write the equation in standard form that is in y equal a a x^2 + BX + C in this form what would you do how can we find a b and c now we need to set u... Read More

Key Insights

• 😫 Writing quadratic equations requires setting up a system of equations and solving for the variables using elimination or substitution.
• 💁 Factoring and completing the square are important techniques to convert equations between different forms.
• 😥 Checking the given points helps confirm the accuracy of the quadratic equation and validates the calculations.
• 👈 Different situations, such as given points, x-intercepts, and vertex coordinates, require different approaches to write the quadratic equation in the desired form.

Questions & Answers

Q: How can you write a quadratic equation in standard form using three given points?

Start by substituting the given points into the standard form equation and setting up a system of equations. Solve for a, b, and c using elimination or substitution. Substituting the values of a, b, and c into the standard form equation will give you the quadratic equation.

Q: What is the process for converting a quadratic equation from standard form to vertex form?

To convert to vertex form, complete the square by factoring out the coefficient of x^2, adding the square of half of the linear term, and adjusting the equation to maintain equality. Simplify the equation in vertex form by combining like terms. Check the vertex coordinates to confirm accuracy.

Q: How can you write a quadratic equation in factored form using two x-intercepts and another point?

Using the factored form equation (y = a(x - h)(x - k)), substitute the x-intercepts into the equation to solve for a. Plug the value of a into the equation and simplify to obtain the quadratic equation in factored form. Expand the equation to standard form by multiplying the terms.

Q: What is the importance of checking if the given points satisfy the quadratic equation?

Checking if the given points satisfy the equation confirms the accuracy of the equation. It ensures that the equation accurately represents the relationship between x and y. This step is crucial to ensure the correctness of the calculations and the validity of the equation.

Summary & Key Takeaways

• To write a quadratic equation in standard form (y = ax^2 + bx + c), plug in the given points and set up a system of equations with a, b, and c as variables.

• Use elimination to solve for a and b. Plug the values of a and b into one of the equations to find the value of c.

• Substitute the values of a, b, and c into the standard form equation to obtain the quadratic equation. Confirm the equation by checking if it satisfies the given points.

• To convert the equation to vertex form (y = a(x - h)^2 + k), complete the square by factoring out the coefficient of x^2, adding the square of half of the linear term, and adjusting the equation to maintain equality.

• Simplify the equation in vertex form and check the vertex coordinates to ensure accuracy.

• An alternative method involves factoring the equation when the x-intercepts are given, writing it in factored form, and then expanding it to standard form.

• Verify the equation by substituting the given points and checking if they satisfy the equation.