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

Grade 11th Grade · Math · 60 min

What's Included

Learning Objective

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

Warm-Up Video

Professor Dave Explains · 6:55

Solving Quadratics by Using the Quadratic Formula

Guided Notes

3 key concepts

1
The quadratic formula is useful because you can plug in the coefficients of the expression and get the solution.
2
The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a].
3
If the discriminant (b² - 4ac) is a negative number, there are no real solutions to the quadratic.

Practice Questions

12 questions · Multiple choice & Short answer

Exit Ticket

Quick comprehension check

“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

What's Included

Learning Objective

Warm-Up Video

Guided Notes

Practice Questions

Exit Ticket

Teacher Guide

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Finding Area of Composite Figures

Calculating Area of Polygons

Finding Area of Rectangles and Squares

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