What is the quadratic formula used for?

The quadratic formula is used to find the solutions (roots) of any quadratic equation in the form Ax² + Bx + C = 0.

In the quadratic formula, x = (-B ± √(B² - 4AC)) / 2A, what is the discriminant and what does it indicate about the solutions of the quadratic equation?

The discriminant is B² - 4AC. If it's positive, there are two distinct real solutions; if it's zero, there is exactly one real solution; and if it's negative, there are no real solutions.

What is the first step in deriving the quadratic formula from the general quadratic equation Ax² + Bx + C = 0?

Divide the entire equation by A, resulting in x² + (B/A)x + (C/A) = 0.

Explain the relationship between factoring a quadratic equation and finding its solutions using the quadratic formula.

Factoring and the quadratic formula are both methods to find the solutions (roots) of a quadratic equation. If a quadratic equation can be easily factored, it provides a quick way to find the solutions. The quadratic formula can be used for any quadratic equation, regardless of whether it is easily factorable.

Solving Quadratic Equations

11th GradeMath60 min

Learning Objective

I can solve quadratic equations using factoring, completing the square, and the quadratic formula.

Lesson Flow

Watch Video

7 min

Solving Quadratics by Using the Quadratic Formula

Professor Dave Explains

Guided Notes

12 min

Key concepts students will learn:

•
The quadratic formula is useful because you can plug in the coefficients of the expression and get the solution.
•
The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a].
•
If the discriminant (b² - 4ac) is a negative number, there are no real solutions to the quadratic.

Practice

18 min

12 questions • Multiple choice & Short answer

Exit Ticket

5 min

“Solve the following quadratic equation using the quadratic formula: x² + 5x + 6 = 0. Show each step, including identifying the values of a, b, and c.”

Teacher Guide

Get the complete package:

Answer keys for all questions
Differentiation strategies
Extension activities
Printable student handouts

Solving Quadratic Equations

Learning Objective

Lesson Flow

Watch Video

Guided Notes

Practice

Exit Ticket

Teacher Guide

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Equivalent Fractions with Models

Finding x with Triangle Angles

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